diff --git a/doc/whatsnew/fragments/7661.bugfix b/doc/whatsnew/fragments/7661.bugfix
new file mode 100644
index 0000000000..2e58c861bb
--- /dev/null
+++ b/doc/whatsnew/fragments/7661.bugfix
@@ -0,0 +1,3 @@
+Fix crash that happened when parsing files with unexpected encoding starting with 'utf' like ``utf13``.
+
+Closes #7661
diff --git a/pylint/checkers/unicode.py b/pylint/checkers/unicode.py
index b5123ef17c..35a0cd7fce 100644
--- a/pylint/checkers/unicode.py
+++ b/pylint/checkers/unicode.py
@@ -218,7 +218,7 @@ def _normalize_codec_name(codec: str) -> str:
 
 def _remove_bom(encoded: bytes, encoding: str) -> bytes:
     """Remove the bom if given from a line."""
-    if not encoding.startswith("utf"):
+    if encoding not in UNICODE_BOMS:
         return encoded
     bom = UNICODE_BOMS[encoding]
     if encoded.startswith(bom):
diff --git a/tests/regrtest_data/encoding/bad_missing_num.py b/tests/regrtest_data/encoding/bad_missing_num.py
new file mode 100644
index 0000000000..a43139838d
--- /dev/null
+++ b/tests/regrtest_data/encoding/bad_missing_num.py
@@ -0,0 +1 @@
+# -*- encoding: utf -*-
diff --git a/tests/regrtest_data/encoding/bad_wrong_num.py b/tests/regrtest_data/encoding/bad_wrong_num.py
new file mode 100644
index 0000000000..5c6bfe7868
--- /dev/null
+++ b/tests/regrtest_data/encoding/bad_wrong_num.py
@@ -0,0 +1 @@
+# -*- encoding: utf-9 -*-
diff --git a/tests/regrtest_data/encoding/good.py b/tests/regrtest_data/encoding/good.py
new file mode 100644
index 0000000000..dae354a675
--- /dev/null
+++ b/tests/regrtest_data/encoding/good.py
@@ -0,0 +1 @@
+# -*- encoding: utf-8 -*-
diff --git a/tests/test_self.py b/tests/test_self.py
index 632022668a..65b76f6612 100644
--- a/tests/test_self.py
+++ b/tests/test_self.py
@@ -148,7 +148,9 @@ def _clean_paths(output: str) -> str:
         output = re.sub(CLEAN_PATH, "", output, flags=re.MULTILINE)
         return output.replace("\\", "/")
 
-    def _test_output(self, args: list[str], expected_output: str) -> None:
+    def _test_output(
+        self, args: list[str], expected_output: str, unexpected_output: str = ""
+    ) -> None:
         out = StringIO()
         args = _add_rcfile_default_pylintrc(args)
         self._run_pylint(args, out=out)
@@ -156,6 +158,9 @@ def _test_output(self, args: list[str], expected_output: str) -> None:
         expected_output = self._clean_paths(expected_output)
         assert expected_output.strip() in actual_output.strip()
 
+        if unexpected_output:
+            assert unexpected_output.strip() not in actual_output.strip()
+
     def _test_output_file(
         self, args: list[str], filename: LocalPath, expected_output: str
     ) -> None:
@@ -1196,6 +1201,20 @@ def test_syntax_error_invalid_encoding(self) -> None:
         expected_output = "unknown encoding"
         self._test_output([module, "-E"], expected_output=expected_output)
 
+    @pytest.mark.parametrize(
+        "module_name,expected_output",
+        [
+            ("good.py", ""),
+            ("bad_wrong_num.py", "(syntax-error)"),
+            ("bad_missing_num.py", "(bad-file-encoding)"),
+        ],
+    )
+    def test_encoding(self, module_name: str, expected_output: str) -> None:
+        path = join(HERE, "regrtest_data", "encoding", module_name)
+        self._test_output(
+            [path], expected_output=expected_output, unexpected_output="(astroid-error)"
+        )
+
 
 class TestCallbackOptions:
     """Test for all callback options we support."""