diff --git a/pandas/core/dtypes/common.py b/pandas/core/dtypes/common.py
index 14184f044ae95..2469f2a1927ed 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -1231,6 +1231,46 @@ def needs_i8_conversion(arr_or_dtype) -> bool:
     )
 
 
+def np_issubclass_compat(unique_dtype, dtypes_set) -> bool:
+    """
+    Check whether the provided dtype is a subclass of, or has an attribute
+    (e.g. _is_numeric) indiciating it is a subclass of any of the dtypes in
+    dtypes_set.
+
+    Parameters
+    ----------
+    unique_dtype : dtype
+        The dtype to check.
+    dtypes_set : array-like
+        The dtypes to check unique_dtype is a sublass of.
+
+    Returns
+    -------
+    boolean
+        Whether or not the unique_dtype is a subclass of dtype_set.
+
+    Examples
+    --------
+    >>> np_issubclass_compat(pd.Int16Dtype(), [np.bool_, np.float])
+    False
+    >>> np_issubclass_compat(pd.Int16Dtype(), [np.integer])
+    True
+    >>> np_issubclass_compat(pd.BooleanDtype(), [np.bool_])
+    True
+    >>> np_issubclass_compat(pd.Float64Dtype(), [np.float])
+    True
+    >>> np_issubclass_compat(pd.Float64Dtype(), [np.number])
+    True
+    """
+    if issubclass(unique_dtype.type, tuple(dtypes_set)) or (
+        np.number in dtypes_set
+        and hasattr(unique_dtype, "_is_numeric")  # is an extensionarray
+        and unique_dtype._is_numeric
+    ):
+        return True
+    return False
+
+
 def is_numeric_dtype(arr_or_dtype) -> bool:
     """
     Check whether the provided array or dtype is of a numeric dtype.
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 0314bdc4ee8ed..50855769f17ec 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -112,6 +112,7 @@
     is_scalar,
     is_sequence,
     needs_i8_conversion,
+    np_issubclass_compat,
     pandas_dtype,
 )
 from pandas.core.dtypes.missing import isna, notna
@@ -3580,6 +3581,7 @@ def select_dtypes(self, include=None, exclude=None) -> DataFrame:
         4   True  1.0
         5  False  2.0
         """
+
         if not is_list_like(include):
             include = (include,) if include is not None else ()
         if not is_list_like(exclude):
@@ -3610,13 +3612,7 @@ def extract_unique_dtypes_from_dtypes_set(
             extracted_dtypes = [
                 unique_dtype
                 for unique_dtype in unique_dtypes
-                # error: Argument 1 to "tuple" has incompatible type
-                # "FrozenSet[Union[ExtensionDtype, str, Any, Type[str],
-                # Type[float], Type[int], Type[complex], Type[bool]]]";
-                # expected "Iterable[Union[type, Tuple[Any, ...]]]"
-                if issubclass(
-                    unique_dtype.type, tuple(dtypes_set)  # type: ignore[arg-type]
-                )
+                if np_issubclass_compat(unique_dtype, dtypes_set)
             ]
             return extracted_dtypes
 
diff --git a/pandas/tests/extension/test_select_dtypes_numeric.py b/pandas/tests/extension/test_select_dtypes_numeric.py
new file mode 100644
index 0000000000000..b65ef9f3b2b03
--- /dev/null
+++ b/pandas/tests/extension/test_select_dtypes_numeric.py
@@ -0,0 +1,50 @@
+import numpy as np
+
+from pandas.core.dtypes.dtypes import ExtensionDtype
+
+import pandas as pd
+from pandas.core.arrays import ExtensionArray
+
+
+class DummyDtype(ExtensionDtype):
+    type = int
+
+    def __init__(self, numeric):
+        self._numeric = numeric
+
+    @property
+    def name(self):
+        return "Dummy"
+
+    @property
+    def _is_numeric(self):
+        return self._numeric
+
+
+class DummyArray(ExtensionArray):
+    def __init__(self, data, dtype):
+        self.data = data
+        self._dtype = dtype
+
+    def __array__(self, dtype):
+        return self.data
+
+    @property
+    def dtype(self):
+        return self._dtype
+
+    def __len__(self) -> int:
+        return len(self.data)
+
+    def __getitem__(self, item):
+        pass
+
+
+def test_select_dtypes_numeric():
+    da = DummyArray([1, 2], dtype=DummyDtype(numeric=True))
+    df = pd.DataFrame(da)
+    assert df.select_dtypes(np.number).shape == df.shape
+
+    da = DummyArray([1, 2], dtype=DummyDtype(numeric=False))
+    df = pd.DataFrame(da)
+    assert df.select_dtypes(np.number).shape != df.shape
diff --git a/pandas/tests/frame/methods/test_select_dtypes.py b/pandas/tests/frame/methods/test_select_dtypes.py
index 4599761909c33..509c5c754af34 100644
--- a/pandas/tests/frame/methods/test_select_dtypes.py
+++ b/pandas/tests/frame/methods/test_select_dtypes.py
@@ -1,9 +1,46 @@
 import numpy as np
 import pytest
 
+from pandas.core.dtypes.dtypes import ExtensionDtype
+
 import pandas as pd
 from pandas import DataFrame, Timestamp
 import pandas._testing as tm
+from pandas.core.arrays import ExtensionArray
+
+
+class DummyDtype(ExtensionDtype):
+    type = int
+
+    def __init__(self, numeric):
+        self._numeric = numeric
+
+    @property
+    def name(self):
+        return "Dummy"
+
+    @property
+    def _is_numeric(self):
+        return self._numeric
+
+
+class DummyArray(ExtensionArray):
+    def __init__(self, data, dtype):
+        self.data = data
+        self._dtype = dtype
+
+    def __array__(self, dtype):
+        return self.data
+
+    @property
+    def dtype(self):
+        return self._dtype
+
+    def __len__(self) -> int:
+        return len(self.data)
+
+    def __getitem__(self, item):
+        pass
 
 
 class TestSelectDtypes:
@@ -324,3 +361,13 @@ def test_select_dtypes_typecodes(self):
         expected = df
         FLOAT_TYPES = list(np.typecodes["AllFloat"])
         tm.assert_frame_equal(df.select_dtypes(FLOAT_TYPES), expected)
+
+    def test_select_dtypes_numeric(self):
+        # GH 35340
+        da = DummyArray([1, 2], dtype=DummyDtype(numeric=True))
+        df = pd.DataFrame(da)
+        assert df.select_dtypes(np.number).shape == df.shape
+
+        da = DummyArray([1, 2], dtype=DummyDtype(numeric=False))
+        df = pd.DataFrame(da)
+        assert df.select_dtypes(np.number).shape != df.shape