diff --git a/python/python/lancedb/functions.py b/python/python/lancedb/functions.py
index 380625f57..5f26b590e 100644
--- a/python/python/lancedb/functions.py
+++ b/python/python/lancedb/functions.py
@@ -26,6 +26,7 @@ import re
 import sys
 import textwrap
 import types
+import warnings
 from collections.abc import Mapping, Sequence
 from datetime import date, datetime
 from typing import (
@@ -1527,9 +1528,14 @@ class _SourcePackager:
         return f"{name} = {_literal_source(value)}"
 
     def _require_importable(self, module_name: str) -> None:
-        """Refuse an import the Function's environment has no way to satisfy:
-        a module that lives in a local source tree, is not shipped with
-        ``code=``, and names no declared package."""
+        """Warn about an import the Function's environment likely cannot
+        satisfy: a module that lives in a local source tree, is not shipped
+        with ``code=``, and names no declared package.
+
+        A warning rather than an error: a distribution name need not match
+        the module it installs, so a declared package can still provide the
+        module, and callers may rewrite the packaged source before
+        registering it."""
         top = module_name.partition(".")[0]
         if (
             top in self._code_modules
@@ -1543,10 +1549,12 @@ class _SourcePackager:
         roots = _installed_roots()
         if not locations or any(location.startswith(roots) for location in locations):
             return
-        raise ValueError(
+        warnings.warn(
             f"@udf source imports {module_name!r} from {locations[0]}, a local "
-            "module the Function's environment cannot import; ship it with "
-            f"code=[{top}] or declare the package that provides it in pip/conda"
+            "module the Function's environment may not be able to import; ship "
+            f"it with code=[{top}] or declare the package that provides it in "
+            "pip/conda",
+            UserWarning,
         )
 
 
@@ -1991,8 +1999,9 @@ def udf(
       place.
 
     A reference to a module in a local source tree that is neither shipped
-    with ``code`` nor provided by a declared package is rejected at
-    registration. Closures, lambdas, nested definitions, mutable module-level
+    with ``code`` nor named by a declared package draws a warning at
+    registration, because the worker will most likely fail to import it.
+    Closures, lambdas, nested definitions, mutable module-level
     objects, code that reaches the module namespace another way
     (``globals()``/``eval``, ``sys.modules``, ``builtins``), and a
     non-standard ``__builtins__`` are rejected where they can be seen and
diff --git a/python/python/tests/test_function_packaging.py b/python/python/tests/test_function_packaging.py
index 239d07be1..6e1e1cf43 100644
--- a/python/python/tests/test_function_packaging.py
+++ b/python/python/tests/test_function_packaging.py
@@ -11,6 +11,7 @@ import json
 import subprocess
 import sys
 import textwrap
+import warnings
 from pathlib import Path
 from typing import Annotated, Optional
 
@@ -299,9 +300,11 @@ def test_code_rejects_submodules_duplicates_and_non_modules(helper_package):
                 return value
 
 
-def test_local_module_outside_code_is_rejected_at_registration(
-    tmp_path, helper_package
-):
+def test_local_module_outside_code_warns_at_registration(tmp_path, helper_package):
+    """The worker most likely cannot import a local module that is neither
+    shipped nor declared, but registration still succeeds: a declared
+    distribution may install it under another name, and callers may rewrite
+    the packaged source before registering it."""
     helper_package(
         "fx_local", {"__init__.py": "def normalize(value):\n    return value\n"}
     )
@@ -322,11 +325,14 @@ def test_local_module_outside_code_is_rejected_at_registration(
         )
         return getattr(importlib.import_module(name), name)
 
-    with pytest.raises(ValueError, match=r"local module.*code=\[fx_local\]"):
-        define("fx_uses_local", "")
+    with pytest.warns(UserWarning, match=r"local module.*code=\[fx_local\]"):
+        local = define("fx_uses_local", "")
+    assert "from fx_local import normalize" in artifact(local).decode()
 
     # A declared package that provides the module is trusted to install it.
-    installed = define("fx_uses_installed", "pip=['fx-local==1.0']")
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        installed = define("fx_uses_installed", "pip=['fx-local==1.0']")
     assert "from fx_local import normalize" in artifact(installed).decode()