diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 814dbe999d5c1..37b4a182b6a9d 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -915,6 +915,7 @@ Numeric
 - Bug in :meth:`DataFrame.count` with ``level="foo"`` and index level ``"foo"`` containing NaNs causes segmentation fault (:issue:`21824`)
 - Bug in :meth:`DataFrame.diff` with ``axis=1`` returning incorrect results with mixed dtypes (:issue:`32995`)
 - Bug in :meth:`DataFrame.corr` and :meth:`DataFrame.cov` raising when handling nullable integer columns with ``pandas.NA`` (:issue:`33803`)
+- Bug in arithmetic operations between ``DataFrame`` objects with non-overlapping columns with duplicate labels causing an infinite loop (:issue:`35194`)
 - Bug in :class:`DataFrame` and :class:`Series` addition and subtraction between object-dtype objects and ``datetime64`` dtype objects (:issue:`33824`)
 
 Conversion
diff --git a/pandas/core/ops/__init__.py b/pandas/core/ops/__init__.py
index 5dd94a8af74ac..60f3d23aaed13 100644
--- a/pandas/core/ops/__init__.py
+++ b/pandas/core/ops/__init__.py
@@ -17,6 +17,7 @@
 from pandas.core.dtypes.generic import ABCDataFrame, ABCIndexClass, ABCSeries
 from pandas.core.dtypes.missing import isna
 
+from pandas.core import algorithms
 from pandas.core.construction import extract_array
 from pandas.core.ops.array_ops import (
     arithmetic_op,
@@ -562,10 +563,12 @@ def _frame_arith_method_with_reindex(
     DataFrame
     """
     # GH#31623, only operate on shared columns
-    cols = left.columns.intersection(right.columns)
+    cols, lcols, rcols = left.columns.join(
+        right.columns, how="inner", level=None, return_indexers=True
+    )
 
-    new_left = left[cols]
-    new_right = right[cols]
+    new_left = left.iloc[:, lcols]
+    new_right = right.iloc[:, rcols]
     result = op(new_left, new_right)
 
     # Do the join on the columns instead of using _align_method_FRAME
@@ -573,7 +576,19 @@ def _frame_arith_method_with_reindex(
     join_columns, _, _ = left.columns.join(
         right.columns, how="outer", level=None, return_indexers=True
     )
-    return result.reindex(join_columns, axis=1)
+
+    if result.columns.has_duplicates:
+        # Avoid reindexing with a duplicate axis.
+        # https://github.com/pandas-dev/pandas/issues/35194
+        indexer, _ = result.columns.get_indexer_non_unique(join_columns)
+        indexer = algorithms.unique1d(indexer)
+        result = result._reindex_with_indexers(
+            {1: [join_columns, indexer]}, allow_dups=True
+        )
+    else:
+        result = result.reindex(join_columns, axis=1)
+
+    return result
 
 
 def _maybe_align_series_as_frame(frame: "DataFrame", series: "Series", axis: int):
diff --git a/pandas/tests/frame/test_arithmetic.py b/pandas/tests/frame/test_arithmetic.py
index a6b0ece58b095..e17357e9845b5 100644
--- a/pandas/tests/frame/test_arithmetic.py
+++ b/pandas/tests/frame/test_arithmetic.py
@@ -1552,3 +1552,12 @@ def test_dataframe_operation_with_non_numeric_types(df, col_dtype):
     expected = expected.astype({"b": col_dtype})
     result = df + pd.Series([-1.0], index=list("a"))
     tm.assert_frame_equal(result, expected)
+
+
+def test_arith_reindex_with_duplicates():
+    # https://github.com/pandas-dev/pandas/issues/35194
+    df1 = pd.DataFrame(data=[[0]], columns=["second"])
+    df2 = pd.DataFrame(data=[[0, 0, 0]], columns=["first", "second", "second"])
+    result = df1 + df2
+    expected = pd.DataFrame([[np.nan, 0, 0]], columns=["first", "second", "second"])
+    tm.assert_frame_equal(result, expected)