diff --git a/doc/whats_new/v1.3.rst b/doc/whats_new/v1.3.rst
index 3ef8a7653b5f7..31ebe9e2d21d6 100644
--- a/doc/whats_new/v1.3.rst
+++ b/doc/whats_new/v1.3.rst
@@ -136,6 +136,10 @@ Changelog
   scikit-learn 1.3: retraining with scikit-learn 1.3 is required.
   :pr:`25186` by :user:`Felipe Breve Siola <fsiola>`.
 
+- |Enhancement| :class:`ensemble.BaggingClassifier` and
+  :class:`ensemble.BaggingRegressor` expose the `allow_nan` tag from the
+  underlying estimator. :pr:`25506` by `Thomas Fan`_.
+
 :mod:`sklearn.exception`
 ........................
 - |Feature| Added :class:`exception.InconsistentVersionWarning` which is raised
diff --git a/sklearn/ensemble/_bagging.py b/sklearn/ensemble/_bagging.py
index 4586e55a59f97..d10f89102ea82 100644
--- a/sklearn/ensemble/_bagging.py
+++ b/sklearn/ensemble/_bagging.py
@@ -23,6 +23,7 @@
 from ..utils.random import sample_without_replacement
 from ..utils._param_validation import Interval, HasMethods, StrOptions
 from ..utils.validation import has_fit_parameter, check_is_fitted, _check_sample_weight
+from ..utils._tags import _safe_tags
 from ..utils.parallel import delayed, Parallel
 
 
@@ -981,6 +982,14 @@ def decision_function(self, X):
 
         return decisions
 
+    def _more_tags(self):
+        if self.estimator is None:
+            estimator = DecisionTreeClassifier()
+        else:
+            estimator = self.estimator
+
+        return {"allow_nan": _safe_tags(estimator, "allow_nan")}
+
 
 class BaggingRegressor(RegressorMixin, BaseBagging):
     """A Bagging regressor.
@@ -1261,3 +1270,10 @@ def _set_oob_score(self, X, y):
 
         self.oob_prediction_ = predictions
         self.oob_score_ = r2_score(y, predictions)
+
+    def _more_tags(self):
+        if self.estimator is None:
+            estimator = DecisionTreeRegressor()
+        else:
+            estimator = self.estimator
+        return {"allow_nan": _safe_tags(estimator, "allow_nan")}
diff --git a/sklearn/ensemble/tests/test_bagging.py b/sklearn/ensemble/tests/test_bagging.py
index 330287cefef37..ebe21a594e8eb 100644
--- a/sklearn/ensemble/tests/test_bagging.py
+++ b/sklearn/ensemble/tests/test_bagging.py
@@ -25,6 +25,8 @@
 from sklearn.pipeline import make_pipeline
 from sklearn.feature_selection import SelectKBest
 from sklearn.model_selection import train_test_split
+from sklearn.ensemble import HistGradientBoostingClassifier
+from sklearn.ensemble import HistGradientBoostingRegressor
 from sklearn.datasets import load_diabetes, load_iris, make_hastie_10_2
 from sklearn.utils import check_random_state
 from sklearn.preprocessing import FunctionTransformer, scale
@@ -980,3 +982,17 @@ def test_deprecated_base_estimator_has_decision_function():
     with pytest.warns(FutureWarning, match=warn_msg):
         y_decision = clf.fit(X, y).decision_function(X)
     assert y_decision.shape == (150, 3)
+
+
+@pytest.mark.parametrize(
+    "bagging, expected_allow_nan",
+    [
+        (BaggingClassifier(HistGradientBoostingClassifier(max_iter=1)), True),
+        (BaggingRegressor(HistGradientBoostingRegressor(max_iter=1)), True),
+        (BaggingClassifier(LogisticRegression()), False),
+        (BaggingRegressor(SVR()), False),
+    ],
+)
+def test_bagging_allow_nan_tag(bagging, expected_allow_nan):
+    """Check that bagging inherits allow_nan tag."""
+    assert bagging._get_tags()["allow_nan"] == expected_allow_nan