diff --git a/fuzz/fuzz_seeds/postgres_alter_extension.sql b/fuzz/fuzz_seeds/postgres_alter_extension.sql
index f82cba6b10..4c6cee2443 100644
--- a/fuzz/fuzz_seeds/postgres_alter_extension.sql
+++ b/fuzz/fuzz_seeds/postgres_alter_extension.sql
@@ -20,3 +20,4 @@ ALTER EXTENSION citext DROP TEXT SEARCH PARSER public.pgrm;
 ALTER EXTENSION citext ADD TEXT SEARCH TEMPLATE public.tpl;
 ALTER EXTENSION citext DROP DATABASE db_name;
 ALTER EXTENSION citext ADD EXTENSION other_ext;
+ALTER EXTENSION citext DROP INDEX public.idx;
diff --git a/src/ast/ddl.rs b/src/ast/ddl.rs
index e0247f7b34..5749c3a2ef 100644
--- a/src/ast/ddl.rs
+++ b/src/ast/ddl.rs
@@ -4946,6 +4946,8 @@ pub enum AlterExtensionMember {
     ForeignDataWrapper(Ident),
     /// `FOREIGN TABLE object_name`
     ForeignTable(ObjectName),
+    /// `INDEX object_name`
+    Index(ObjectName),
     /// `[ PROCEDURAL ] LANGUAGE object_name`
     Language {
         /// Whether the `PROCEDURAL` keyword was present.
@@ -5007,6 +5009,7 @@ impl fmt::Display for AlterExtensionMember {
                 write!(f, "FOREIGN DATA WRAPPER {name}")
             }
             AlterExtensionMember::ForeignTable(name) => write!(f, "FOREIGN TABLE {name}"),
+            AlterExtensionMember::Index(name) => write!(f, "INDEX {name}"),
             AlterExtensionMember::Language { procedural, name } => {
                 if *procedural {
                     write!(f, "PROCEDURAL LANGUAGE {name}")
diff --git a/src/parser/mod.rs b/src/parser/mod.rs
index 9230c03ec3..bbf4e1d60d 100644
--- a/src/parser/mod.rs
+++ b/src/parser/mod.rs
@@ -12563,6 +12563,8 @@ impl<'a> Parser<'a> {
             Ok(AlterExtensionMember::ForeignTable(
                 self.parse_object_name(false)?,
             ))
+        } else if self.parse_keyword(Keyword::INDEX) {
+            Ok(AlterExtensionMember::Index(self.parse_object_name(false)?))
         } else if self.parse_keywords(&[Keyword::PROCEDURAL, Keyword::LANGUAGE]) {
             Ok(AlterExtensionMember::Language {
                 procedural: true,
diff --git a/tests/sqlparser_postgres.rs b/tests/sqlparser_postgres.rs
index 0626ae2093..86814d30c2 100644
--- a/tests/sqlparser_postgres.rs
+++ b/tests/sqlparser_postgres.rs
@@ -13538,6 +13538,7 @@ fn alter_extension_member_round_trip_forms(action: &str) {
         format!("ALTER EXTENSION ext_name {action} FOREIGN DATA WRAPPER fdw"),
         format!("ALTER EXTENSION ext_name {action} FOREIGN TABLE ft"),
         format!("ALTER EXTENSION ext_name {action} FOREIGN TABLE schema.ft"),
+        format!("ALTER EXTENSION ext_name {action} INDEX idx"),
         format!("ALTER EXTENSION ext_name {action} LANGUAGE plpgsql"),
         format!("ALTER EXTENSION ext_name {action} PROCEDURAL LANGUAGE plpgsql"),
         format!("ALTER EXTENSION ext_name {action} MATERIALIZED VIEW mv"),
@@ -13734,6 +13735,7 @@ fn parse_alter_extension_add_member() {
         "EXTENSION",
         "FOREIGN DATA WRAPPER",
         "FOREIGN TABLE",
+        "INDEX",
         "LANGUAGE",
         "MATERIALIZED VIEW",
         "PROCEDURAL LANGUAGE",