diff --git a/modin/core/io/text/text_file_dispatcher.py b/modin/core/io/text/text_file_dispatcher.py
index 158212b37ec..75f05356bb1 100644
--- a/modin/core/io/text/text_file_dispatcher.py
+++ b/modin/core/io/text/text_file_dispatcher.py
@@ -683,6 +683,9 @@ def check_parameters_support(
         if read_kwargs["chunksize"] is not None:
             return (False, "`chunksize` parameter is not supported")
 
+        if read_kwargs.get("iterator"):
+            return (False, "`iterator==True` parameter is not supported")
+
         if read_kwargs.get("dialect") is not None:
             return (False, "`dialect` parameter is not supported")
 
diff --git a/modin/pandas/test/test_io.py b/modin/pandas/test/test_io.py
index d28aca0294e..6e93954a358 100644
--- a/modin/pandas/test/test_io.py
+++ b/modin/pandas/test/test_io.py
@@ -614,6 +614,16 @@ def test_read_csv_iteration(self, iterator):
 
         df_equals(modin_df, pd_df)
 
+        # Tests #6553
+        if iterator:
+            rdf_reader = pd.read_csv(filename, iterator=iterator)
+            pd_reader = pandas.read_csv(filename, iterator=iterator)
+
+            modin_df = rdf_reader.read()
+            pd_df = pd_reader.read()
+
+            df_equals(modin_df, pd_df)
+
     def test_read_csv_encoding_976(self):
         file_name = "modin/pandas/test/data/issue_976.csv"
         names = [str(i) for i in range(11)]