diff --git a/tiled/_tests/test_writing.py b/tiled/_tests/test_writing.py
index 83813c757..24e4a8dc6 100644
--- a/tiled/_tests/test_writing.py
+++ b/tiled/_tests/test_writing.py
@@ -19,6 +19,8 @@
 from ..client import Context, from_context, record_history
 from ..queries import Key
 from ..server.app import build_app
+
+# from ..server.object_cache import WARNING_PANDAS_BLOCKS
 from ..structures.core import Spec
 from ..structures.data_source import DataSource
 from ..structures.sparse import COOStructure
@@ -112,6 +114,7 @@ def test_write_array_chunked(tree):
         assert result.specs == specs
 
 
+# @pytest.mark.filterwarnings(f"ignore:{WARNING_PANDAS_BLOCKS}:DeprecationWarning")
 def test_write_dataframe_full(tree):
     with Context.from_app(
         build_app(tree, validation_registry=validation_registry)
@@ -137,6 +140,7 @@ def test_write_dataframe_full(tree):
         assert result.specs == specs
 
 
+# @pytest.mark.filterwarnings(f"ignore:{WARNING_PANDAS_BLOCKS}:DeprecationWarning")
 def test_write_dataframe_partitioned(tree):
     with Context.from_app(
         build_app(tree, validation_registry=validation_registry)
@@ -390,6 +394,7 @@ async def test_delete_non_empty_node(tree):
         client.delete("a")
 
 
+# @pytest.mark.filterwarnings(f"ignore:{WARNING_PANDAS_BLOCKS}:DeprecationWarning")
 @pytest.mark.asyncio
 async def test_write_in_container(tree):
     "Create a container and write a structure into it."
diff --git a/tiled/server/object_cache.py b/tiled/server/object_cache.py
index c6813aadb..8ad55a972 100644
--- a/tiled/server/object_cache.py
+++ b/tiled/server/object_cache.py
@@ -13,6 +13,8 @@
 import cachey
 from dask.callbacks import Callback
 
+from ..utils import catch_warning_msg
+
 if __debug__:
     import logging
 
@@ -23,6 +25,19 @@
     logger.addHandler(handler)
 
 
+# See https://github.com/bluesky/tiled/issues/675#issuecomment-1983581882
+WARNING_PANDAS_BLOCKS = (
+    "DataFrame._data is deprecated and will be removed in a future version. "
+    "Use public APIs instead."
+)
+
+
+def catch_pandas_blocks_warning():
+    return catch_warning_msg(
+        action="ignore", message=WARNING_PANDAS_BLOCKS, category=DeprecationWarning
+    )
+
+
 class _NO_CACHE_SENTINEL:
     def __init__(self):
         self.dask_context = contextlib.nullcontext()
@@ -129,7 +144,8 @@ def put(self, key, value, cost, nbytes=None):
             Computed (with best effort) if not provided.
         """
         if nbytes is None:
-            nbytes = self._cache.get_nbytes(value)
+            with catch_pandas_blocks_warning():
+                nbytes = self._cache.get_nbytes(value)
         logger.debug("Store %r (cost=%.3f, nbytes=%d)", key, cost, nbytes)
         self._cache.put(key, value, cost, nbytes=nbytes)
 
@@ -196,7 +212,8 @@ def _posttask(self, key, value, dsk, state, id):
         if deps:
             duration += max(self.durations.get(k, 0) for k in deps)
         self.durations[key] = duration
-        nb = self._nbytes(value)
+        with catch_pandas_blocks_warning():
+            nb = self._nbytes(value)
         self.cache.put(("dask", *key), value, cost=duration, nbytes=nb)
 
     def _finish(self, dsk, state, errored):
diff --git a/tiled/utils.py b/tiled/utils.py
index 17f7c38e7..558017c3f 100644
--- a/tiled/utils.py
+++ b/tiled/utils.py
@@ -3,6 +3,7 @@
 import collections.abc
 import contextlib
 import enum
+import functools
 import importlib
 import importlib.util
 import inspect
@@ -12,6 +13,7 @@
 import re
 import sys
 import threading
+import warnings
 from pathlib import Path
 from typing import Any, Callable
 from urllib.parse import urlparse, urlunparse
@@ -709,3 +711,39 @@ def ensure_uri(uri_or_path):
             mutable[1] = "localhost"
             uri_str = urlunparse(mutable)
     return str(uri_str)
+
+
+class catch_warning_msg(warnings.catch_warnings):
+    """Backward compatible version of catch_warnings for python <3.11.
+
+    Allows regex matching of warning message, as in filterwarnings().
+    Note that this context manager is not thread-safe.
+    https://docs.python.org/3.12/library/warnings.html#warnings.catch_warnings
+    """
+
+    def __init__(
+        self,
+        *,
+        action="",
+        message="",
+        category=Warning,
+        module="",
+        lineno=0,
+        append=False,
+        record=False,
+    ):
+        super().__init__(record=record)
+        self.apply_filter = functools.partial(
+            warnings.filterwarnings,
+            action,
+            message=message,
+            category=category,
+            module=module,
+            lineno=lineno,
+            append=append,
+        )
+
+    def __enter__(self):
+        super().__enter__()
+        self.apply_filter()
+        return self