diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 27b16cb706e8d..0ac17c69ba452 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -594,6 +594,7 @@ Styler
 Other
 ^^^^^
 - Bug in :class:`DataFrame` when passing a ``dict`` with a NA scalar and ``columns`` that would always return ``np.nan`` (:issue:`57205`)
+- Bug in :func:`eval` on :class:`ExtensionArray` on including division ``/`` failed with a ``TypeError``. (:issue:`58748`)
 - Bug in :func:`eval` where the names of the :class:`Series` were not preserved when using ``engine="numexpr"``. (:issue:`10239`)
 - Bug in :func:`unique` on :class:`Index` not always returning :class:`Index` (:issue:`57043`)
 - Bug in :meth:`DataFrame.eval` and :meth:`DataFrame.query` which caused an exception when using NumPy attributes via ``@`` notation, e.g., ``df.eval("@np.floor(a)")``. (:issue:`58041`)
diff --git a/pandas/core/computation/ops.py b/pandas/core/computation/ops.py
index b7a1cb173f659..d69765e91f467 100644
--- a/pandas/core/computation/ops.py
+++ b/pandas/core/computation/ops.py
@@ -19,6 +19,7 @@
 
 from pandas.core.dtypes.common import (
     is_list_like,
+    is_numeric_dtype,
     is_scalar,
 )
 
@@ -508,10 +509,6 @@ def _disallow_scalar_only_bool_ops(self) -> None:
             raise NotImplementedError("cannot evaluate scalar only bool ops")
 
 
-def isnumeric(dtype) -> bool:
-    return issubclass(np.dtype(dtype).type, np.number)
-
-
 class Div(BinOp):
     """
     Div operator to special case casting.
@@ -525,7 +522,9 @@ class Div(BinOp):
     def __init__(self, lhs, rhs) -> None:
         super().__init__("/", lhs, rhs)
 
-        if not isnumeric(lhs.return_type) or not isnumeric(rhs.return_type):
+        if not is_numeric_dtype(lhs.return_type) or not is_numeric_dtype(
+            rhs.return_type
+        ):
             raise TypeError(
                 f"unsupported operand type(s) for {self.op}: "
                 f"'{lhs.return_type}' and '{rhs.return_type}'"
diff --git a/pandas/tests/frame/test_query_eval.py b/pandas/tests/frame/test_query_eval.py
index 643d342b052a4..ff1bf5632e920 100644
--- a/pandas/tests/frame/test_query_eval.py
+++ b/pandas/tests/frame/test_query_eval.py
@@ -202,6 +202,13 @@ def test_eval_simple(self, engine, parser):
         expected = df["a"]
         tm.assert_series_equal(expected, res)
 
+    def test_extension_array_eval(self, engine, parser):
+        # GH#58748
+        df = DataFrame({"a": pd.array([1, 2, 3]), "b": pd.array([4, 5, 6])})
+        result = df.eval("a / b", engine=engine, parser=parser)
+        expected = Series([0.25, 0.40, 0.50])
+        tm.assert_series_equal(result, expected)
+
 
 class TestDataFrameQueryWithMultiIndex:
     def test_query_with_named_multiindex(self, parser, engine):