diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 45f8344a1ebe0..5b58ba14a1eff 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -273,6 +273,7 @@ I/O
 - Allow custom error values for parse_dates argument of :func:`read_sql`, :func:`read_sql_query` and :func:`read_sql_table` (:issue:`35185`)
 - Bug in :func:`to_hdf` raising ``KeyError`` when trying to apply
   for subclasses of ``DataFrame`` or ``Series`` (:issue:`33748`).
+- Bug in :meth:`~HDFStore.put` raising a wrong ``TypeError`` when saving a DataFrame with non-string dtype (:issue:`34274`)
 - Bug in :func:`json_normalize` resulting in the first element of a generator object not being included in the returned ``DataFrame`` (:issue:`35923`)
 - Bug in :func:`read_excel` forward filling :class:`MultiIndex` names with multiple header and index columns specified (:issue:`34673`)
 - :func:`pandas.read_excel` now respects :func:``pandas.set_option`` (:issue:`34252`)
diff --git a/pandas/io/pytables.py b/pandas/io/pytables.py
index ceaf6e1ac21e5..d2b02038f8b78 100644
--- a/pandas/io/pytables.py
+++ b/pandas/io/pytables.py
@@ -3915,6 +3915,7 @@ def _create_axes(
                 nan_rep=nan_rep,
                 encoding=self.encoding,
                 errors=self.errors,
+                block_columns=b_items,
             )
             adj_name = _maybe_adjust_name(new_name, self.version)
 
@@ -4878,7 +4879,14 @@ def _unconvert_index(
 
 
 def _maybe_convert_for_string_atom(
-    name: str, block: "Block", existing_col, min_itemsize, nan_rep, encoding, errors
+    name: str,
+    block: "Block",
+    existing_col,
+    min_itemsize,
+    nan_rep,
+    encoding,
+    errors,
+    block_columns: List[str],
 ):
     if not block.is_object:
         return block.values
@@ -4912,14 +4920,20 @@ def _maybe_convert_for_string_atom(
 
         # we cannot serialize this data, so report an exception on a column
         # by column basis
-        for i in range(len(block.shape[0])):
+
+        # expected behaviour:
+        # search block for a non-string object column by column
+        for i in range(block.shape[0]):
             col = block.iget(i)
             inferred_type = lib.infer_dtype(col, skipna=False)
             if inferred_type != "string":
-                iloc = block.mgr_locs.indexer[i]
+                error_column_label = (
+                    block_columns[i] if len(block_columns) > i else f"No.{i}"
+                )
                 raise TypeError(
-                    f"Cannot serialize the column [{iloc}] because\n"
-                    f"its data contents are [{inferred_type}] object dtype"
+                    f"Cannot serialize the column [{error_column_label}]\n"
+                    f"because its data contents are not [string] but "
+                    f"[{inferred_type}] object dtype"
                 )
 
     # itemsize is the maximum length of a string (along any dimension)
diff --git a/pandas/tests/io/pytables/test_store.py b/pandas/tests/io/pytables/test_store.py
index 7e288ec6f5063..3f0fd6e7483f8 100644
--- a/pandas/tests/io/pytables/test_store.py
+++ b/pandas/tests/io/pytables/test_store.py
@@ -2055,7 +2055,10 @@ def test_append_raise(self, setup_path):
             df = tm.makeDataFrame()
             df["invalid"] = [["a"]] * len(df)
             assert df.dtypes["invalid"] == np.object_
-            msg = re.escape("object of type 'int' has no len()")
+            msg = re.escape(
+                """Cannot serialize the column [invalid]
+because its data contents are not [string] but [mixed] object dtype"""
+            )
             with pytest.raises(TypeError, match=msg):
                 store.append("df", df)
 
@@ -2221,7 +2224,10 @@ def test_unimplemented_dtypes_table_columns(self, setup_path):
 
         with ensure_clean_store(setup_path) as store:
             # this fails because we have a date in the object block......
-            msg = "object of type 'int' has no len()"
+            msg = re.escape(
+                """Cannot serialize the column [datetime1]
+because its data contents are not [string] but [date] object dtype"""
+            )
             with pytest.raises(TypeError, match=msg):
                 store.append("df_unimplemented", df)