diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 7a177344a42c7..9a524db89de85 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -74,12 +74,12 @@ enhancement2
 Other enhancements
 ^^^^^^^^^^^^^^^^^^
 
+- :attr:`Series.attrs` / :attr:`DataFrame.attrs` now uses a deepcopy for propagating ``attrs`` (:issue:`54134`).
 - :func:`read_csv` now supports ``on_bad_lines`` parameter with ``engine="pyarrow"``. (:issue:`54480`)
 - :meth:`ExtensionArray._explode` interface method added to allow extension type implementations of the ``explode`` method (:issue:`54833`)
 - :meth:`ExtensionArray.duplicated` added to allow extension type implementations of the ``duplicated`` method (:issue:`55255`)
 - DataFrame.apply now allows the usage of numba (via ``engine="numba"``) to JIT compile the passed function, allowing for potential speedups (:issue:`54666`)
 - Implement masked algorithms for :meth:`Series.value_counts` (:issue:`54984`)
--
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_220.notable_bug_fixes:
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 738f4cbe6bc43..2e6c8919eff38 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -2,6 +2,7 @@
 from __future__ import annotations
 
 import collections
+from copy import deepcopy
 import datetime as dt
 from functools import partial
 import gc
@@ -368,6 +369,13 @@ def attrs(self) -> dict[Hashable, Any]:
         --------
         DataFrame.flags : Global flags applying to this object.
 
+        Notes
+        -----
+        Many operations that create new datasets will copy ``attrs``. Copies
+        are always deep so that changing ``attrs`` will only affect the
+        present dataset. ``pandas.concat`` copies ``attrs`` only if all input
+        datasets have the same ``attrs``.
+
         Examples
         --------
         For Series:
@@ -6191,8 +6199,12 @@ def __finalize__(self, other, method: str | None = None, **kwargs) -> Self:
                stable across pandas releases.
         """
         if isinstance(other, NDFrame):
-            for name in other.attrs:
-                self.attrs[name] = other.attrs[name]
+            if other.attrs:
+                # We want attrs propagation to have minimal performance
+                # impact if attrs are not used; i.e. attrs is an empty dict.
+                # One could make the deepcopy unconditionally, but a deepcopy
+                # of an empty dict is 50x more expensive than the empty check.
+                self.attrs = deepcopy(other.attrs)
 
             self.flags.allows_duplicate_labels = other.flags.allows_duplicate_labels
             # For subclasses using _metadata.
@@ -6201,11 +6213,13 @@ def __finalize__(self, other, method: str | None = None, **kwargs) -> Self:
                 object.__setattr__(self, name, getattr(other, name, None))
 
         if method == "concat":
-            attrs = other.objs[0].attrs
-            check_attrs = all(objs.attrs == attrs for objs in other.objs[1:])
-            if check_attrs:
-                for name in attrs:
-                    self.attrs[name] = attrs[name]
+            # propagate attrs only if all concat arguments have the same attrs
+            if all(bool(obj.attrs) for obj in other.objs):
+                # all concatenate arguments have non-empty attrs
+                attrs = other.objs[0].attrs
+                have_same_attrs = all(obj.attrs == attrs for obj in other.objs[1:])
+                if have_same_attrs:
+                    self.attrs = deepcopy(attrs)
 
             allows_duplicate_labels = all(
                 x.flags.allows_duplicate_labels for x in other.objs
diff --git a/pandas/tests/frame/test_api.py b/pandas/tests/frame/test_api.py
index 8fc78629beb0a..06bf169bf4dbc 100644
--- a/pandas/tests/frame/test_api.py
+++ b/pandas/tests/frame/test_api.py
@@ -315,6 +315,15 @@ def test_attrs(self):
         result = df.rename(columns=str)
         assert result.attrs == {"version": 1}
 
+    def test_attrs_deepcopy(self):
+        df = DataFrame({"A": [2, 3]})
+        assert df.attrs == {}
+        df.attrs["tags"] = {"spam", "ham"}
+
+        result = df.rename(columns=str)
+        assert result.attrs == df.attrs
+        assert result.attrs["tags"] is not df.attrs["tags"]
+
     @pytest.mark.parametrize("allows_duplicate_labels", [True, False, None])
     def test_set_flags(
         self, allows_duplicate_labels, frame_or_series, using_copy_on_write