diff --git a/doc/whats_new/upcoming_changes/sklearn.naive_bayes/31556.fix.rst b/doc/whats_new/upcoming_changes/sklearn.naive_bayes/31556.fix.rst
new file mode 100644
index 0000000000000..0f5b969bd9e6f
--- /dev/null
+++ b/doc/whats_new/upcoming_changes/sklearn.naive_bayes/31556.fix.rst
@@ -0,0 +1,3 @@
+- :class:`naive_bayes.CategoricalNB` now correctly declares that it accepts
+  categorical features in the tags returned by its `__sklearn_tags__` method.
+  By :user:`Olivier Grisel <ogrisel>`
diff --git a/sklearn/naive_bayes.py b/sklearn/naive_bayes.py
index e5b03abbb903a..31a1b87af2916 100644
--- a/sklearn/naive_bayes.py
+++ b/sklearn/naive_bayes.py
@@ -1433,6 +1433,7 @@ def partial_fit(self, X, y, classes=None, sample_weight=None):
 
     def __sklearn_tags__(self):
         tags = super().__sklearn_tags__()
+        tags.input_tags.categorical = True
         tags.input_tags.sparse = False
         tags.input_tags.positive_only = True
         return tags
diff --git a/sklearn/tests/test_naive_bayes.py b/sklearn/tests/test_naive_bayes.py
index 99cfe030a940f..f5638e7384e86 100644
--- a/sklearn/tests/test_naive_bayes.py
+++ b/sklearn/tests/test_naive_bayes.py
@@ -968,3 +968,12 @@ def test_predict_joint_proba(Estimator, global_random_seed):
     log_prob_x = logsumexp(jll, axis=1)
     log_prob_x_y = jll - np.atleast_2d(log_prob_x).T
     assert_allclose(est.predict_log_proba(X2), log_prob_x_y)
+
+
+@pytest.mark.parametrize("Estimator", ALL_NAIVE_BAYES_CLASSES)
+def test_categorical_input_tag(Estimator):
+    tags = Estimator().__sklearn_tags__()
+    if Estimator is CategoricalNB:
+        assert tags.input_tags.categorical
+    else:
+        assert not tags.input_tags.categorical
diff --git a/sklearn/utils/_test_common/instance_generator.py b/sklearn/utils/_test_common/instance_generator.py
index 221236f8bc998..8d88ad23eb5e9 100644
--- a/sklearn/utils/_test_common/instance_generator.py
+++ b/sklearn/utils/_test_common/instance_generator.py
@@ -144,7 +144,6 @@
     MultiOutputRegressor,
     RegressorChain,
 )
-from sklearn.naive_bayes import CategoricalNB
 from sklearn.neighbors import (
     KernelDensity,
     KNeighborsClassifier,
@@ -898,15 +897,6 @@ def _yield_instances_for_check(check, estimator_orig):
             "sample_weight is not equivalent to removing/repeating samples."
         ),
     },
-    CategoricalNB: {
-        # TODO: fix sample_weight handling of this estimator, see meta-issue #16298
-        "check_sample_weight_equivalence_on_dense_data": (
-            "sample_weight is not equivalent to removing/repeating samples."
-        ),
-        "check_sample_weight_equivalence_on_sparse_data": (
-            "sample_weight is not equivalent to removing/repeating samples."
-        ),
-    },
     ColumnTransformer: {
         "check_estimators_empty_data_messages": "FIXME",
         "check_estimators_nan_inf": "FIXME",
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 156448698a780..ccff3cb44cad5 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -3997,7 +3997,10 @@ def check_positive_only_tag_during_fit(name, estimator_orig):
     y = _enforce_estimator_tags_y(estimator, y)
     set_random_state(estimator, 0)
     X = _enforce_estimator_tags_X(estimator, X)
-    X -= X.mean()
+    # Make sure that the dtype of X stays unchanged: for instance estimator
+    # that expect categorical inputs typically expected integer-based encoded
+    # categories.
+    X -= X.mean().astype(X.dtype)
 
     if tags.input_tags.positive_only:
         with raises(ValueError, match="Negative values in data"):