diff --git a/python-package/xgboost/data.py b/python-package/xgboost/data.py
index ea63ef9c8..e11b5f067 100644
--- a/python-package/xgboost/data.py
+++ b/python-package/xgboost/data.py
@@ -231,13 +231,15 @@ _pandas_dtype_mapper = {
     "Int16": "int",
     "Int32": "int",
     "Int64": "int",
+    "Float32": "float",
+    "Float64": "float",
     "boolean": "i",
 }
 
 
 _ENABLE_CAT_ERR = (
-    "When categorical type is supplied, DMatrix parameter `enable_categorical` must "
-    "be set to `True`."
+    "When categorical type is supplied, The experimental DMatrix parameter"
+    "`enable_categorical` must be set to `True`."
 )
 
 
@@ -246,7 +248,7 @@ def _invalid_dataframe_dtype(data: DataType) -> None:
     # cudf series doesn't have `dtypes`.
     if hasattr(data, "dtypes") and hasattr(data.dtypes, "__iter__"):
         bad_fields = [
-            str(data.columns[i])
+            f"{data.columns[i]}: {dtype}"
             for i, dtype in enumerate(data.dtypes)
             if dtype.name not in _pandas_dtype_mapper
         ]
@@ -296,13 +298,20 @@ def _pandas_feature_info(
 
 def is_nullable_dtype(dtype: PandasDType) -> bool:
     """Wether dtype is a pandas nullable type."""
-    from pandas.api.types import is_integer_dtype, is_bool_dtype
+    from pandas.api.types import (
+        is_integer_dtype,
+        is_bool_dtype,
+        is_float_dtype,
+        is_categorical_dtype,
+    )
+
     # dtype: pd.core.arrays.numeric.NumericDtype
-    nullable_alias = {"Int16", "Int32", "Int64"}
+    nullable_alias = {"Int16", "Int32", "Int64", "Float32", "Float64", "category"}
     is_int = is_integer_dtype(dtype) and dtype.name in nullable_alias
     # np.bool has alias `bool`, while pd.BooleanDtype has `bzoolean`.
     is_bool = is_bool_dtype(dtype) and dtype.name == "boolean"
-    return is_int or is_bool
+    is_float = is_float_dtype(dtype) and dtype.name in nullable_alias
+    return is_int or is_bool or is_float or is_categorical_dtype(dtype)
 
 
 def _pandas_cat_null(data: DataFrame) -> DataFrame:
@@ -353,7 +362,7 @@ def _transform_pandas_df(
     if not all(
         dtype.name in _pandas_dtype_mapper
         or is_sparse(dtype)
-        or is_nullable_dtype(dtype)
+        or (is_nullable_dtype(dtype) and not is_categorical_dtype(dtype))
         or (is_categorical_dtype(dtype) and enable_categorical)
         for dtype in data.dtypes
     ):
diff --git a/tests/python/test_with_pandas.py b/tests/python/test_with_pandas.py
index 1401dd699..e4289c1cd 100644
--- a/tests/python/test_with_pandas.py
+++ b/tests/python/test_with_pandas.py
@@ -330,3 +330,35 @@ class TestPandas:
         b0 = test_bool(pd.BooleanDtype())
         b1 = test_bool(bool)
         assert b0 != b1         # None is converted to False with np.bool
+
+        data = {"f0": [1.0, 2.0, None, 3.0], "f1": [3.0, 2.0, None, 1.0]}
+
+        arr = np.array([data["f0"], data["f1"]]).T
+        Xy = xgb.DMatrix(arr, y)
+        Xy.feature_types = None
+        Xy.feature_names = None
+        from_np = to_bytes(Xy)
+
+        def test_float(dtype) -> bytes:
+            arr = pd.DataFrame(data, dtype=dtype)
+            Xy = xgb.DMatrix(arr, y)
+            Xy.feature_types = None
+            Xy.feature_names = None
+            return to_bytes(Xy)
+
+        b0 = test_float(pd.Float64Dtype())
+        b1 = test_float(float)
+        assert b0 == b1         # both are converted to NaN
+        assert b0 == from_np
+
+        def test_cat(dtype) -> bytes:
+            arr = pd.DataFrame(data, dtype=dtype)
+            if dtype is None:
+                arr = arr.astype("category")
+            Xy = xgb.DMatrix(arr, y, enable_categorical=True)
+            Xy.feature_types = None
+            return to_bytes(Xy)
+
+        b0 = test_cat(pd.CategoricalDtype())
+        b1 = test_cat(None)
+        assert b0 == b1