diff --git a/modin/core/io/column_stores/parquet_dispatcher.py b/modin/core/io/column_stores/parquet_dispatcher.py
index 6596ead087d..294245e63f8 100644
--- a/modin/core/io/column_stores/parquet_dispatcher.py
+++ b/modin/core/io/column_stores/parquet_dispatcher.py
@@ -285,19 +285,33 @@ def files(self):
     def to_pandas_dataframe(self, columns):
         return self.dataset.to_pandas(columns=columns)
 
+    # Karthik Velayutham writes:
+    #
+    # fastparquet doesn't have a nice method like PyArrow, so we
+    # have to copy some of their logic here while we work on getting
+    # an easier method to get a list of valid files.
+    # See: https://github.com/dask/fastparquet/issues/795
     def _get_fastparquet_files(self):  # noqa: GL08
-        # fastparquet doesn't have a nice method like PyArrow, so we
-        # have to copy some of their logic here while we work on getting
-        # an easier method to get a list of valid files.
-        # See: https://github.com/dask/fastparquet/issues/795
         if "*" in self.path:
             files = self.fs.glob(self.path)
         else:
-            files = [
-                f
-                for f in self.fs.find(self.path)
-                if f.endswith(".parquet") or f.endswith(".parq")
-            ]
+            # (Resolving issue #6778)
+            #
+            # Users will pass in a directory to a delta table, which stores parquet
+            # files in various directories along with other, non-parquet files. We
+            # need to identify those parquet files and not the non-parquet files.
+            #
+            # However, we also need to support users passing in explicit files that
+            # don't necessarily have the `.parq` or `.parquet` extension -- if a user
+            # says that a file is parquet, then we should probably give it a shot.
+            if os.path.isfile(self.path):
+                files = self.fs.find(self.path)
+            else:
+                files = [
+                    f
+                    for f in self.fs.find(self.path)
+                    if f.endswith(".parquet") or f.endswith(".parq")
+                ]
         return files
 
 
diff --git a/modin/pandas/test/test_io.py b/modin/pandas/test/test_io.py
index 672bd3a8003..ddac2748847 100644
--- a/modin/pandas/test/test_io.py
+++ b/modin/pandas/test/test_io.py
@@ -1464,6 +1464,20 @@ def comparator(df1, df2):
                 comparator=comparator,
             )
 
+    # Tests issue #6778
+    def test_read_parquet_no_extension(self, engine, make_parquet_file):
+        with ensure_clean(".parquet") as unique_filename:
+            # Remove the .parquet extension
+            no_ext_fname = unique_filename[:unique_filename.index(".parquet")]
+
+            make_parquet_file(filename=no_ext_fname)
+            eval_io(
+                fn_name="read_parquet",
+                # read_parquet kwargs
+                engine=engine,
+                path=no_ext_fname
+            )
+
     @pytest.mark.parametrize(
         "filters",
         [None, [], [("col1", "==", 5)], [("col1", "<=", 215), ("col2", ">=", 35)]],