diff --git a/changes/4029.bugfix.md b/changes/4029.bugfix.md
new file mode 100644
index 0000000000..b4abda7658
--- /dev/null
+++ b/changes/4029.bugfix.md
@@ -0,0 +1,8 @@
+`zarr.storage` is no longer replaced by a `ModuleType` subclass at import time.
+The subclass only existed to warn about the long-deprecated
+`zarr.storage.default_compressor` attribute, but serializers that dispatch on
+the exact type of an object (such as `cloudpickle`, which Dask uses by default)
+could not serialize the module and raised
+`TypeError: cannot pickle 'VerboseModule' object`. Setting
+`zarr.storage.default_compressor` no longer emits a deprecation warning; use
+`zarr.config` to configure `array.v2_default_compressor` instead.
diff --git a/pyproject.toml b/pyproject.toml
index c68450474e..98bdb0ab9c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -109,6 +109,7 @@ homepage = "https://github.com/zarr-developers/zarr-python"
 # pins deliberately, e.g. via dependabot or `uv lock --upgrade`.
 [dependency-groups]
 test = [
+    "cloudpickle==3.1.2",
     "coverage==7.16.2",
     "pytest==9.1.1",
     "pytest-asyncio==1.4.0",
diff --git a/src/zarr/storage/__init__.py b/src/zarr/storage/__init__.py
index f1bd1724af..1c41082ba7 100644
--- a/src/zarr/storage/__init__.py
+++ b/src/zarr/storage/__init__.py
@@ -1,9 +1,3 @@
-import sys
-import warnings
-from types import ModuleType
-from typing import Any
-
-from zarr.errors import ZarrDeprecationWarning
 from zarr.storage._common import StoreLike, StorePath
 from zarr.storage._fsspec import FsspecStore
 from zarr.storage._local import LocalStore
@@ -26,20 +20,3 @@
     "WrapperStore",
     "ZipStore",
 ]
-
-
-class VerboseModule(ModuleType):
-    def __setattr__(self, attr: str, value: Any) -> None:
-        if attr == "default_compressor":
-            warnings.warn(
-                "setting zarr.storage.default_compressor is deprecated, use "
-                "zarr.config to configure array.v2_default_compressor "
-                "e.g. config.set({'codecs.zstd':'numcodecs.Zstd', 'array.v2_default_compressor.numeric': 'zstd'})",
-                ZarrDeprecationWarning,
-                stacklevel=1,
-            )
-        else:
-            super().__setattr__(attr, value)
-
-
-sys.modules[__name__].__class__ = VerboseModule
diff --git a/tests/test_store/test_core.py b/tests/test_store/test_core.py
index daf62e3843..c928ba8417 100644
--- a/tests/test_store/test_core.py
+++ b/tests/test_store/test_core.py
@@ -1,8 +1,10 @@
 import tempfile
 from collections.abc import Awaitable, Callable, Generator
 from pathlib import Path
+from types import ModuleType
 from typing import Any, Literal
 
+import cloudpickle
 import pytest
 from packaging.version import parse as parse_version
 
@@ -434,3 +436,15 @@ def test_different_open_mode(tmp_path: Path) -> None:
         match="Store is not read-only but mode is 'r'. Unable to create a read-only copy of the store. Please use a read-only store or a storage class that implements .with_read_only().",
     ):
         zarr.open_array(store=zip_store, path="a", zarr_format=2, mode="r")
+
+
+def test_storage_module_is_picklable() -> None:
+    # `zarr.storage` used to be swapped for a `VerboseModule` subclass of
+    # `types.ModuleType` in order to warn about the long-deprecated
+    # `zarr.storage.default_compressor` attribute. cloudpickle dispatches on the
+    # exact type of an object, so the subclass was not registered and
+    # serializing the module raised `TypeError: cannot pickle 'VerboseModule'
+    # object`, which broke passing `zarr.storage.ObjectStore` around with Dask.
+    # See issue #4029.
+    assert type(zarr.storage) is ModuleType
+    assert cloudpickle.loads(cloudpickle.dumps(zarr.storage)) is zarr.storage
diff --git a/tests/test_v2.py b/tests/test_v2.py
index 2e04339441..9a36aca74b 100644
--- a/tests/test_v2.py
+++ b/tests/test_v2.py
@@ -20,7 +20,6 @@
 from zarr.core.dtype.wrapper import ZDType
 from zarr.core.group import Group
 from zarr.core.sync import sync
-from zarr.errors import ZarrDeprecationWarning
 from zarr.storage import MemoryStore, StorePath
 
 
@@ -225,11 +224,6 @@ def test_v2_non_contiguous(numpy_order: Literal["C", "F"], zarr_order: Literal["
         assert (sub_arr).flags.c_contiguous
 
 
-def test_default_compressor_deprecation_warning() -> None:
-    with pytest.warns(ZarrDeprecationWarning, match="default_compressor is deprecated"):
-        zarr.storage.default_compressor = "zarr.codecs.zstd.ZstdCodec()"  # type: ignore[attr-defined]
-
-
 @pytest.mark.parametrize("fill_value", [None, (b"", 0, 0.0)], ids=["no_fill", "fill"])
 def test_structured_dtype_roundtrip(fill_value: float | bytes, tmp_path: Path) -> None:
     a = np.array(
diff --git a/uv.lock b/uv.lock
index b14033c5b4..7bbcce0ca0 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,5 +1,5 @@
 version = 1
-revision = 3
+revision = 5
 requires-python = ">=3.12"
 resolution-markers = [
     "python_full_version >= '3.15'",
@@ -604,6 +604,15 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/ae/44/c1221527f6a71a01ec6fbad7fa78f1d50dfa02217385cf0fa3eec7087d59/click-8.3.3-py3-none-any.whl", hash = "sha256:a2bf429bb3033c89fa4936ffb35d5cb471e3719e1f3c8a7c3fff0b8314305613", size = 110502, upload-time = "2026-04-22T15:11:25.044Z" },
 ]
 
+[[package]]
+name = "cloudpickle"
+version = "3.1.2"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/27/fb/576f067976d320f5f0114a8d9fa1215425441bb35627b1993e5afd8111e5/cloudpickle-3.1.2.tar.gz", hash = "sha256:7fda9eb655c9c230dab534f1983763de5835249750e85fbcef43aaa30a9a2414", size = 22330, upload-time = "2025-11-03T09:25:26.604Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/88/39/799be3f2f0f38cc727ee3b4f1445fe6d5e4133064ec2e4115069418a5bb6/cloudpickle-3.1.2-py3-none-any.whl", hash = "sha256:9acb47f6afd73f60dc1df93bb801b472f05ff42fa6c84167d25cb206be1fbf4a", size = 22228, upload-time = "2025-11-03T09:25:25.534Z" },
+]
+
 [[package]]
 name = "colorama"
 version = "0.4.6"
@@ -3670,6 +3679,7 @@ remote = [
 dev = [
     { name = "astroid" },
     { name = "botocore" },
+    { name = "cloudpickle" },
     { name = "coverage" },
     { name = "fsspec" },
     { name = "griffe-inherited-docstrings" },
@@ -3723,6 +3733,7 @@ release = [
 ]
 remote-tests = [
     { name = "botocore" },
+    { name = "cloudpickle" },
     { name = "coverage" },
     { name = "fsspec" },
     { name = "hypothesis" },
@@ -3743,6 +3754,7 @@ remote-tests = [
     { name = "uv" },
 ]
 test = [
+    { name = "cloudpickle" },
     { name = "coverage" },
     { name = "hypothesis" },
     { name = "numpydoc" },
@@ -3780,6 +3792,7 @@ provides-extras = ["cast-value-rs", "cli", "gpu", "optional", "remote"]
 dev = [
     { name = "astroid", specifier = "==4.3.3" },
     { name = "botocore" },
+    { name = "cloudpickle", specifier = "==3.1.2" },
     { name = "coverage", specifier = "==7.16.2" },
     { name = "fsspec", specifier = ">=2023.10.0" },
     { name = "griffe-inherited-docstrings", specifier = "==1.1.3" },
@@ -3831,6 +3844,7 @@ docs = [
 release = [{ name = "towncrier", specifier = "==26.9.0" }]
 remote-tests = [
     { name = "botocore" },
+    { name = "cloudpickle", specifier = "==3.1.2" },
     { name = "coverage", specifier = "==7.16.2" },
     { name = "fsspec", specifier = ">=2023.10.0" },
     { name = "hypothesis", specifier = "==6.168.3" },
@@ -3851,6 +3865,7 @@ remote-tests = [
     { name = "uv", specifier = "==0.12.21" },
 ]
 test = [
+    { name = "cloudpickle", specifier = "==3.1.2" },
     { name = "coverage", specifier = "==7.16.2" },
     { name = "hypothesis", specifier = "==6.168.3" },
     { name = "numpydoc", specifier = "==1.11.0" },