diff --git a/pkg/sql/create_stats.go b/pkg/sql/create_stats.go
index 2eb1f966e9bf..202f114fccc0 100644
--- a/pkg/sql/create_stats.go
+++ b/pkg/sql/create_stats.go
@@ -440,6 +440,12 @@ func createStatsDefaultColumns(
 				colIDs = append(colIDs, col.GetID())
 			}
 
+			// Do not attempt to create multi-column stats with no columns. This
+			// can happen when an index contains only virtual computed columns.
+			if len(colIDs) == 0 {
+				continue
+			}
+
 			// Check for existing stats and remember the requested stats.
 			if !trackStatsIfNotExists(colIDs) {
 				continue
diff --git a/pkg/sql/logictest/testdata/logic_test/distsql_stats b/pkg/sql/logictest/testdata/logic_test/distsql_stats
index 19670a9f777c..a65447da464c 100644
--- a/pkg/sql/logictest/testdata/logic_test/distsql_stats
+++ b/pkg/sql/logictest/testdata/logic_test/distsql_stats
@@ -1218,3 +1218,16 @@ CREATE STATISTICS s ON b FROM t71080;
 
 statement error cannot create statistics on virtual column \"b\"
 CREATE STATISTICS s ON a, b FROM t71080;
+
+# Regression test for #76867. Do not attempt to collect empty multi-column stats
+# when there are indexes on columns that are all virtual.
+statement ok
+CREATE TABLE t76867 (
+  a INT,
+  b INT AS (a + 1) VIRTUAL,
+  c INT AS (a + 2) VIRTUAL,
+  INDEX (b, c)
+)
+
+statement ok
+ANALYZE t76867