diff --git a/feature_engine/wrappers/wrappers.py b/feature_engine/wrappers/wrappers.py
index 37e593a1b..28d336e81 100644
--- a/feature_engine/wrappers/wrappers.py
+++ b/feature_engine/wrappers/wrappers.py
@@ -215,6 +215,7 @@ def fit(self, X: pd.DataFrame, y: Optional[str] = None):
             "OneHotEncoder",
             "OrdinalEncoder",
             "SimpleImputer",
+            "FunctionTransformer",
         ]:
             self.variables_ = _find_all_variables(X, self.variables)
 
diff --git a/tests/test_wrappers/test_sklearn_wrapper.py b/tests/test_wrappers/test_sklearn_wrapper.py
index 30b884f7f..b0db6d9a4 100644
--- a/tests/test_wrappers/test_sklearn_wrapper.py
+++ b/tests/test_wrappers/test_sklearn_wrapper.py
@@ -549,3 +549,31 @@ def test_get_feature_names_out_ohe(varlist, df_vartypes):
         ]
 
         assert output_feat == transformer.get_feature_names_out(varlist)
+
+
+def test_function_transformer_works_with_categoricals():
+    X = pd.DataFrame({"col1": ["1", "2", "3"], "col2": ["a", "b", "c"]})
+
+    X_expected = pd.DataFrame({"col1": [1.0, 2.0, 3.0], "col2": ["a", "b", "c"]})
+
+    transformer = SklearnTransformerWrapper(
+        FunctionTransformer(lambda x: x.astype(np.float64)), variables=["col1"]
+    )
+
+    X_tf = transformer.fit_transform(X)
+
+    pd.testing.assert_frame_equal(X_expected, X_tf)
+
+
+def test_function_transformer_works_with_numericals():
+    X = pd.DataFrame({"col1": [1, 2, 3], "col2": ["a", "b", "c"]})
+
+    X_expected = pd.DataFrame({"col1": [2, 3, 4], "col2": ["a", "b", "c"]})
+
+    transformer = SklearnTransformerWrapper(
+        FunctionTransformer(lambda x: x+1), variables=["col1"]
+    )
+
+    X_tf = transformer.fit_transform(X)
+
+    pd.testing.assert_frame_equal(X_expected, X_tf)