diff --git a/pkg/sql/opt/ordering/project.go b/pkg/sql/opt/ordering/project.go
index 3a87400f2bb8..927c8dacf779 100644
--- a/pkg/sql/opt/ordering/project.go
+++ b/pkg/sql/opt/ordering/project.go
@@ -22,18 +22,15 @@ func projectCanProvideOrdering(expr memo.RelExpr, required *physical.OrderingCho
 	proj := expr.(*memo.ProjectExpr)
 	inputCols := proj.Input.Relational().OutputCols
 
-	if required.CanProjectCols(inputCols) {
-		return true
-	}
-
-	// We may be able to "remap" columns using the internal FD set.
-	if fdSet := proj.InternalFDs(); required.CanSimplify(fdSet) {
-		simplified := required.Copy()
+	// Use a simplified ordering if it exists. This must be kept consistent with
+	// projectBuildChildReqOrdering, which always simplifies the ordering if
+	// possible.
+	simplified := *required
+	if fdSet := proj.InternalFDs(); simplified.CanSimplify(fdSet) {
+		simplified = required.Copy()
 		simplified.Simplify(fdSet)
-		return simplified.CanProjectCols(inputCols)
 	}
-
-	return false
+	return simplified.CanProjectCols(inputCols)
 }
 
 func projectBuildChildReqOrdering(
diff --git a/pkg/sql/opt/ordering/project_test.go b/pkg/sql/opt/ordering/project_test.go
index 73f043765856..7001bbb65b03 100644
--- a/pkg/sql/opt/ordering/project_test.go
+++ b/pkg/sql/opt/ordering/project_test.go
@@ -39,7 +39,7 @@ func TestProject(t *testing.T) {
 
 	input := &testexpr.Instance{
 		Rel: &props.Relational{
-			OutputCols: opt.MakeColSet(1, 2, 3, 4),
+			OutputCols: opt.MakeColSet(1, 2, 3, 4, 6),
 			FuncDeps:   fds,
 		},
 	}
@@ -73,6 +73,14 @@ func TestProject(t *testing.T) {
 			req: "+5",
 			exp: "no",
 		},
+		{
+			// Regression test for #64399. projectCanProvideOrdering should not
+			// return true when the columns remaining in the ordering after
+			// simplification cannot be provided. This causes
+			// projectBuildChildReqOrdering to panic.
+			req: "+(5|6)",
+			exp: "no",
+		},
 	}
 	for _, tc := range testCases {
 		req := physical.ParseOrderingChoice(tc.req)