diff --git a/src/frontend/planner_test/tests/testdata/input/functional_dependency.yaml b/src/frontend/planner_test/tests/testdata/input/functional_dependency.yaml
index e7e53333ef2f4..e5813047f1e49 100644
--- a/src/frontend/planner_test/tests/testdata/input/functional_dependency.yaml
+++ b/src/frontend/planner_test/tests/testdata/input/functional_dependency.yaml
@@ -1,8 +1,15 @@
-- name: test functional dependency for order key pruning
+- name: test functional dependency for order key pruning (order by)
   sql: |
     create table t1 (id int primary key, i int);
     select id, i from t1 order by id, i limit 2;
   expected_outputs:
     - logical_plan
     - stream_plan
-    - batch_plan
\ No newline at end of file
+    - batch_plan
+- name: test functional dependency for order key pruning (index)
+  sql: |
+    create table t1 (v1 int, v2 int);
+    create materialized view v as select count(*) cnt from t1;
+    explain (verbose) create index mv_idx on v(cnt);
+  expected_outputs:
+    - explain_output
diff --git a/src/frontend/planner_test/tests/testdata/output/functional_dependency.yaml b/src/frontend/planner_test/tests/testdata/output/functional_dependency.yaml
index fe6dbbcd8e608..ec76fb1fb341c 100644
--- a/src/frontend/planner_test/tests/testdata/output/functional_dependency.yaml
+++ b/src/frontend/planner_test/tests/testdata/output/functional_dependency.yaml
@@ -1,5 +1,5 @@
 # This file is automatically generated. See `src/frontend/planner_test/README.md` for more information.
-- name: test functional dependency for order key pruning
+- name: test functional dependency for order key pruning (order by)
   sql: |
     create table t1 (id int primary key, i int);
     select id, i from t1 order by id, i limit 2;
@@ -21,3 +21,12 @@
           └─StreamGroupTopN { order: [t1.id ASC], limit: 2, offset: 0, group_key: [_vnode] }
             └─StreamProject { exprs: [t1.id, t1.i, Vnode(t1.id) as _vnode] }
               └─StreamTableScan { table: t1, columns: [t1.id, t1.i], stream_scan_type: ArrangementBackfill, stream_key: [t1.id], pk: [id], dist: UpstreamHashShard(t1.id) }
+- name: test functional dependency for order key pruning (index)
+  sql: |
+    create table t1 (v1 int, v2 int);
+    create materialized view v as select count(*) cnt from t1;
+    explain (verbose) create index mv_idx on v(cnt);
+  explain_output: |
+    StreamMaterialize { columns: [cnt], stream_key: [], pk_columns: [cnt], pk_conflict: NoCheck }
+    └─StreamExchange { dist: HashShard(v.cnt) }
+      └─StreamTableScan { table: v, columns: [v.cnt], stream_scan_type: ArrangementBackfill, stream_key: [], pk: [], dist: Single }
diff --git a/src/frontend/src/optimizer/plan_node/derive.rs b/src/frontend/src/optimizer/plan_node/derive.rs
index aff6bea2be6a3..0d190f27d6ad6 100644
--- a/src/frontend/src/optimizer/plan_node/derive.rs
+++ b/src/frontend/src/optimizer/plan_node/derive.rs
@@ -80,6 +80,7 @@ pub(crate) fn derive_pk(
     input: PlanRef,
     user_order_by: Order,
     columns: &[ColumnCatalog],
+    prune_order_by: bool,
 ) -> (Vec<ColumnOrder>, Vec<usize>) {
     // Note(congyi): avoid pk duplication
     let stream_key = input
@@ -106,8 +107,12 @@ pub(crate) fn derive_pk(
     let mut in_order = FixedBitSet::with_capacity(schema.len());
     let mut pk = vec![];
 
-    let func_dep = input.functional_dependency();
-    let user_order_by = func_dep.minimize_order_key(user_order_by);
+    let user_order_by = if prune_order_by {
+        let func_dep = input.functional_dependency();
+        func_dep.minimize_order_key(user_order_by)
+    } else {
+        user_order_by
+    };
 
     for order in &user_order_by.column_orders {
         let idx = order.column_index;
diff --git a/src/frontend/src/optimizer/plan_node/stream_materialize.rs b/src/frontend/src/optimizer/plan_node/stream_materialize.rs
index 792eaf4d7a068..29870c68f9cc8 100644
--- a/src/frontend/src/optimizer/plan_node/stream_materialize.rs
+++ b/src/frontend/src/optimizer/plan_node/stream_materialize.rs
@@ -222,7 +222,7 @@ impl StreamMaterialize {
             // No order by for create table, so stream key is identical to table pk.
             (table_pk, pk_column_indices)
         } else {
-            derive_pk(input, user_order_by, &columns)
+            derive_pk(input, user_order_by, &columns, table_type != TableType::Index)
         };
         // assert: `stream_key` is a subset of `table_pk`
 
diff --git a/src/frontend/src/optimizer/plan_node/stream_sink.rs b/src/frontend/src/optimizer/plan_node/stream_sink.rs
index 7a724a20be46a..1e1679cc2f682 100644
--- a/src/frontend/src/optimizer/plan_node/stream_sink.rs
+++ b/src/frontend/src/optimizer/plan_node/stream_sink.rs
@@ -312,7 +312,7 @@ impl StreamSink {
     ) -> Result<(PlanRef, SinkDesc)> {
         let sink_type =
             Self::derive_sink_type(input.append_only(), &properties, format_desc.as_ref())?;
-        let (pk, _) = derive_pk(input.clone(), user_order_by, &columns);
+        let (pk, _) = derive_pk(input.clone(), user_order_by, &columns, true);
         let mut downstream_pk =
             Self::parse_downstream_pk(&columns, properties.get(DOWNSTREAM_PK_KEY))?;
         let mut extra_partition_col_idx = None;
diff --git a/src/frontend/src/optimizer/plan_node/stream_subscription.rs b/src/frontend/src/optimizer/plan_node/stream_subscription.rs
index e9d8936961586..bf4a05b9e93d0 100644
--- a/src/frontend/src/optimizer/plan_node/stream_subscription.rs
+++ b/src/frontend/src/optimizer/plan_node/stream_subscription.rs
@@ -110,7 +110,7 @@ impl StreamSubscription {
         properties: WithOptions,
         user_id: UserId,
     ) -> Result<(PlanRef, SubscriptionCatalog)> {
-        let (pk, _) = derive_pk(input.clone(), user_order_by, &columns);
+        let (pk, _) = derive_pk(input.clone(), user_order_by, &columns, true);
         let required_dist = match input.distribution() {
             Distribution::Single => RequiredDist::single(),
             _ => {