diff --git a/django/db/backends/base/features.py b/django/db/backends/base/features.py
index 1e957d105e..38af239cbe 100644
--- a/django/db/backends/base/features.py
+++ b/django/db/backends/base/features.py
@@ -415,6 +415,10 @@ class BaseDatabaseFeatures:
     # Does the Round() database function round to even?
     rounds_to_even = False
 
+    # Should dollar signs be prohibited in column aliases to prevent SQL
+    # injection?
+    prohibits_dollar_signs_in_column_aliases = False
+
     # A set of dotted paths to tests in Django's test suite that are expected
     # to fail on this database.
     django_test_expected_failures = set()
diff --git a/django/db/backends/postgresql/compiler.py b/django/db/backends/postgresql/compiler.py
index 08d78e333a..48d0ccfd9d 100644
--- a/django/db/backends/postgresql/compiler.py
+++ b/django/db/backends/postgresql/compiler.py
@@ -1,6 +1,6 @@
 from django.db.models.sql.compiler import (  # isort:skip
     SQLAggregateCompiler,
-    SQLCompiler as BaseSQLCompiler,
+    SQLCompiler,
     SQLDeleteCompiler,
     SQLInsertCompiler as BaseSQLInsertCompiler,
     SQLUpdateCompiler,
@@ -25,15 +25,6 @@ class InsertUnnest(list):
         return "UNNEST(%s)" % ", ".join(self)
 
 
-class SQLCompiler(BaseSQLCompiler):
-    def quote_name_unless_alias(self, name):
-        if "$" in name:
-            raise ValueError(
-                "Dollar signs are not permitted in column aliases on PostgreSQL."
-            )
-        return super().quote_name_unless_alias(name)
-
-
 class SQLInsertCompiler(BaseSQLInsertCompiler):
     def assemble_as_sql(self, fields, value_rows):
         # Specialize bulk-insertion of literal values through UNNEST to
diff --git a/django/db/backends/postgresql/features.py b/django/db/backends/postgresql/features.py
index 5e4ed320be..30d06c95c5 100644
--- a/django/db/backends/postgresql/features.py
+++ b/django/db/backends/postgresql/features.py
@@ -70,6 +70,7 @@ class DatabaseFeatures(BaseDatabaseFeatures):
     supports_nulls_distinct_unique_constraints = True
     supports_no_precision_decimalfield = True
     can_rename_index = True
+    prohibits_dollar_signs_in_column_aliases = True
     test_collations = {
         "deterministic": "C",
         "non_default": "sv-x-icu",
diff --git a/django/db/models/sql/compiler.py b/django/db/models/sql/compiler.py
index 20f06ad168..9068d87a89 100644
--- a/django/db/models/sql/compiler.py
+++ b/django/db/models/sql/compiler.py
@@ -553,6 +553,14 @@ class SQLCompiler:
         for table names. This avoids problems with some SQL dialects that treat
         quoted strings specially (e.g. PostgreSQL).
         """
+        if (
+            self.connection.features.prohibits_dollar_signs_in_column_aliases
+            and "$" in name
+        ):
+            raise ValueError(
+                "Dollar signs are not permitted in column aliases on "
+                f"{self.connection.display_name}."
+            )
         if name in self.quote_cache:
             return self.quote_cache[name]
         if (
diff --git a/tests/annotations/tests.py b/tests/annotations/tests.py
index 10cd05db63..6336cabafa 100644
--- a/tests/annotations/tests.py
+++ b/tests/annotations/tests.py
@@ -1545,8 +1545,11 @@ class AliasTests(TestCase):
         qs = Book.objects.alias(
             **{"crafted_alia$": FilteredRelation("authors")}
         ).values("name", "crafted_alia$")
-        if connection.vendor == "postgresql":
-            msg = "Dollar signs are not permitted in column aliases on PostgreSQL."
+        if connection.features.prohibits_dollar_signs_in_column_aliases:
+            msg = (
+                "Dollar signs are not permitted in column aliases on "
+                f"{connection.display_name}."
+            )
             with self.assertRaisesMessage(ValueError, msg):
                 list(qs)
         else: