diff --git a/src/openai/lib/_pydantic.py b/src/openai/lib/_pydantic.py
index 3cfe224cb1..d4c18d2325 100644
--- a/src/openai/lib/_pydantic.py
+++ b/src/openai/lib/_pydantic.py
@@ -47,8 +47,14 @@ def _ensure_strict_json_schema(
             _ensure_strict_json_schema(definition_schema, path=(*path, "definitions", definition_name), root=root)
 
     typ = json_schema.get("type")
-    if typ == "object" and "additionalProperties" not in json_schema:
-        json_schema["additionalProperties"] = False
+    if typ == "object":
+        # Set additionalProperties to False for strict schema compliance, but preserve
+        # structured schemas (e.g., for Dict[str, T] which needs {"additionalProperties": {schema}}).
+        # The OpenAI API requires additionalProperties=false for structured output,
+        # even if Pydantic models use extra="allow" which sets it to True.
+        additional_props = json_schema.get("additionalProperties")
+        if additional_props is True or "additionalProperties" not in json_schema:
+            json_schema["additionalProperties"] = False
 
     # object types
     # { 'type': 'object', 'properties': { 'a':  {...} } }
diff --git a/tests/lib/test_pydantic.py b/tests/lib/test_pydantic.py
index 754a15151c..f784921a7b 100644
--- a/tests/lib/test_pydantic.py
+++ b/tests/lib/test_pydantic.py
@@ -409,3 +409,29 @@ def test_nested_inline_ref_expansion() -> None:
                 "additionalProperties": False,
             }
         )
+
+
+def test_pydantic_extra_allow() -> None:
+    """Test that models with extra='allow' correctly set additionalProperties to False.
+
+    Regression test for issue #2740.
+    The OpenAI API requires additionalProperties=false for structured output,
+    even when Pydantic models use extra="allow" which generates True by default.
+    """
+    from pydantic import ConfigDict
+
+    class MyClassWithExtraAllow(BaseModel):
+        model_config = ConfigDict(extra="allow")
+        field: str = Field(description="A test field")
+
+    schema = to_strict_json_schema(MyClassWithExtraAllow)
+
+    assert schema == snapshot(
+        {
+            "properties": {"field": {"description": "A test field", "title": "Field", "type": "string"}},
+            "required": ["field"],
+            "title": "MyClassWithExtraAllow",
+            "type": "object",
+            "additionalProperties": False,
+        }
+    )