diff --git a/pkg/sql/create_stats.go b/pkg/sql/create_stats.go
index 217496594a2e..ea6d189e6baf 100644
--- a/pkg/sql/create_stats.go
+++ b/pkg/sql/create_stats.go
@@ -247,6 +247,13 @@ func (n *createStatsNode) makeJobRecord(ctx context.Context) (*jobs.Record, erro
 
 		columnIDs := make([]descpb.ColumnID, len(columns))
 		for i := range columns {
+			if columns[i].IsVirtual() {
+				return nil, pgerror.Newf(
+					pgcode.InvalidColumnReference,
+					"cannot create statistics on virtual column %q",
+					columns[i].ColName(),
+				)
+			}
 			columnIDs[i] = columns[i].GetID()
 		}
 		col, err := tableDesc.FindColumnWithID(columnIDs[0])
@@ -441,9 +448,16 @@ func createStatsDefaultColumns(
 				continue
 			}
 
-			colIDs := make([]descpb.ColumnID, j+1)
+			colIDs := make([]descpb.ColumnID, 0, j+1)
 			for k := 0; k <= j; k++ {
-				colIDs[k] = idx.GetKeyColumnID(k)
+				col, err := desc.FindColumnWithID(idx.GetKeyColumnID(k))
+				if err != nil {
+					return nil, err
+				}
+				if col.IsVirtual() {
+					continue
+				}
+				colIDs = append(colIDs, col.GetID())
 			}
 
 			// Check for existing stats and remember the requested stats.
diff --git a/pkg/sql/logictest/testdata/logic_test/distsql_stats b/pkg/sql/logictest/testdata/logic_test/distsql_stats
index f2dbb4c26d1c..9ce0693ed1a4 100644
--- a/pkg/sql/logictest/testdata/logic_test/distsql_stats
+++ b/pkg/sql/logictest/testdata/logic_test/distsql_stats
@@ -824,11 +824,18 @@ upper_bound  range_rows  distinct_range_rows  equal_rows
 3            0           0                    1
 
 # Test that stats are not collected for virtual columns.
+statement ok
+SET CLUSTER SETTING sql.stats.multi_column_collection.enabled = true
+
 statement ok
 CREATE TABLE virt (
   a INT,
+  b INT,
   v INT AS (a + 10) VIRTUAL,
-  INDEX (v)
+  INDEX (v),
+  INDEX (a, v),
+  INDEX (a, v, b),
+  INDEX (a) WHERE v > 0
 )
 
 statement ok
@@ -850,7 +857,9 @@ ORDER BY
   column_names::STRING, created
 ----
 statistics_name  column_names  row_count  null_count  has_histogram
+s                {a,b}         3          0           false
 s                {a}           3          0           true
+s                {b}           3          3           true
 s                {rowid}       3          0           true
 
 # Test that stats are not collect for inaccessible virtual columns that
@@ -861,7 +870,9 @@ CREATE TABLE expression (
   b INT,
   j JSON,
   INDEX a_plus_b ((a + b)),
-  INVERTED INDEX j_a ((j->'a'))
+  INDEX a_a_plus_b (a, (a + b)),
+  INVERTED INDEX j_a ((j->'a')),
+  INVERTED INDEX a_j_a (a, (j->'a'))
 );
 INSERT INTO expression VALUES (1, 1, '{"a": "b"}'), (2, 10, '{"c": "d"}'), (3, 1, '{"e": "f"}');
 
@@ -1037,6 +1048,7 @@ ORDER BY
 column_names  has_histogram
 {id}          true
 {j}           true
+{s,j}         false
 {s}           true
 
 statement ok
@@ -1181,3 +1193,28 @@ CREATE TABLE t63387 (
 );
 INSERT INTO t63387 VALUES (1, '{}');
 CREATE STATISTICS s FROM t63387;
+
+# Regression test for #71080. Stats collection should succeed on tables with NOT
+# NULL virtual columns.
+statement ok
+SET CLUSTER SETTING sql.stats.multi_column_collection.enabled = true
+
+statement ok
+CREATE TABLE t71080 (
+  k INT PRIMARY KEY,
+  a INT,
+  b INT NOT NULL AS (a + 10) VIRTUAL,
+  INDEX (a, b)
+);
+
+statement ok
+INSERT INTO t71080 VALUES (1, 2);
+
+statement ok
+CREATE STATISTICS s FROM t71080;
+
+statement error cannot create statistics on virtual column \"b\"
+CREATE STATISTICS s ON b FROM t71080;
+
+statement error cannot create statistics on virtual column \"b\"
+CREATE STATISTICS s ON a, b FROM t71080;