diff --git a/src/backend/distributed/commands/statistics.c b/src/backend/distributed/commands/statistics.c
index b43f6335ef4..7a77b6b3dd8 100644
--- a/src/backend/distributed/commands/statistics.c
+++ b/src/backend/distributed/commands/statistics.c
@@ -69,7 +69,15 @@ PreprocessCreateStatisticsStmt(Node *node, const char *queryString,
 {
 	CreateStatsStmt *stmt = castNode(CreateStatsStmt, node);
 
-	RangeVar *relation = (RangeVar *) linitial(stmt->relations);
+	Node *relationNode = (Node *) linitial(stmt->relations);
+
+	if (!IsA(relationNode, RangeVar))
+	{
+		return NIL;
+	}
+
+	RangeVar *relation = (RangeVar *) relationNode;
+
 	Oid relationId = RangeVarGetRelid(relation, ShareUpdateExclusiveLock, false);
 
 	if (!IsCitusTable(relationId) || !ShouldPropagate())
diff --git a/src/backend/distributed/deparser/qualify_statistics_stmt.c b/src/backend/distributed/deparser/qualify_statistics_stmt.c
index 7a99e6dfad3..7243762dc79 100644
--- a/src/backend/distributed/deparser/qualify_statistics_stmt.c
+++ b/src/backend/distributed/deparser/qualify_statistics_stmt.c
@@ -34,7 +34,14 @@ QualifyCreateStatisticsStmt(Node *node)
 {
 	CreateStatsStmt *stmt = castNode(CreateStatsStmt, node);
 
-	RangeVar *relation = (RangeVar *) linitial(stmt->relations);
+	Node *relationNode = (Node *) linitial(stmt->relations);
+
+	if (!IsA(relationNode, RangeVar))
+	{
+		return;
+	}
+
+	RangeVar *relation = (RangeVar *) relationNode;
 
 	if (relation->schemaname == NULL)
 	{
diff --git a/src/test/regress/expected/pg16.out b/src/test/regress/expected/pg16.out
index d7c39a9fddc..72d7b7312b9 100644
--- a/src/test/regress/expected/pg16.out
+++ b/src/test/regress/expected/pg16.out
@@ -4,6 +4,17 @@
 SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 16 AS server_version_ge_16
 \gset
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+ERROR:  CREATE STATISTICS only supports relation names in the FROM clause
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+ERROR:  CREATE STATISTICS only supports relation names in the FROM clause
+DROP FUNCTION tftest;
 \if :server_version_ge_16
 \else
 \q
diff --git a/src/test/regress/expected/pg16_0.out b/src/test/regress/expected/pg16_0.out
index 730c916cadc..f8d8d68800d 100644
--- a/src/test/regress/expected/pg16_0.out
+++ b/src/test/regress/expected/pg16_0.out
@@ -4,6 +4,17 @@
 SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 16 AS server_version_ge_16
 \gset
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+ERROR:  only a single relation is allowed in CREATE STATISTICS
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+ERROR:  only a single relation is allowed in CREATE STATISTICS
+DROP FUNCTION tftest;
 \if :server_version_ge_16
 \else
 \q
diff --git a/src/test/regress/expected/pg17.out b/src/test/regress/expected/pg17.out
index aa27ae85a88..24b449578cf 100644
--- a/src/test/regress/expected/pg17.out
+++ b/src/test/regress/expected/pg17.out
@@ -4,6 +4,19 @@
 SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 17 AS server_version_ge_17
 \gset
+
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+ERROR:  CREATE STATISTICS only supports relation names in the FROM clause
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+ERROR:  CREATE STATISTICS only supports relation names in the FROM clause
+DROP FUNCTION tftest;
+
 -- PG17 has the capabilty to pull up a correlated ANY subquery to a join if
 -- the subquery only refers to its immediate parent query. Previously, the
 -- subquery needed to be implemented as a SubPlan node, typically as a
diff --git a/src/test/regress/expected/pg17_0.out b/src/test/regress/expected/pg17_0.out
index 6f65f60993b..0dabb1e2c0a 100644
--- a/src/test/regress/expected/pg17_0.out
+++ b/src/test/regress/expected/pg17_0.out
@@ -4,6 +4,19 @@
 SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 17 AS server_version_ge_17
 \gset
+
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+ERROR:  only a single relation is allowed in CREATE STATISTICS
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+ERROR:  only a single relation is allowed in CREATE STATISTICS
+DROP FUNCTION tftest;
+
 -- PG17 has the capabilty to pull up a correlated ANY subquery to a join if
 -- the subquery only refers to its immediate parent query. Previously, the
 -- subquery needed to be implemented as a SubPlan node, typically as a
diff --git a/src/test/regress/sql/pg16.sql b/src/test/regress/sql/pg16.sql
index ec4eb3fc736..c9137c8f315 100644
--- a/src/test/regress/sql/pg16.sql
+++ b/src/test/regress/sql/pg16.sql
@@ -4,6 +4,18 @@
 SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 16 AS server_version_ge_16
 \gset
+
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+DROP FUNCTION tftest;
+
 \if :server_version_ge_16
 \else
 \q
diff --git a/src/test/regress/sql/pg17.sql b/src/test/regress/sql/pg17.sql
index 60ea6d9e7e1..4f0a8459129 100644
--- a/src/test/regress/sql/pg17.sql
+++ b/src/test/regress/sql/pg17.sql
@@ -5,6 +5,17 @@ SHOW server_version \gset
 SELECT substring(:'server_version', '\d+')::int >= 17 AS server_version_ge_17
 \gset
 
+-- test invalid statistics
+-- behavior is same among PG versions, error message differs
+-- relevant PG16 commits: d84a6c3dad1 and f30c04682cd
+CREATE STATISTICS tst ON a FROM (VALUES (x)) AS foo;
+
+CREATE FUNCTION tftest(int) returns table(a int, b int) as $$
+SELECT $1, $1+i FROM generate_series(1,5) g(i);
+$$ LANGUAGE sql IMMUTABLE STRICT;
+CREATE STATISTICS alt_stat2 ON a FROM tftest(1);
+DROP FUNCTION tftest;
+
 -- PG17 has the capabilty to pull up a correlated ANY subquery to a join if
 -- the subquery only refers to its immediate parent query. Previously, the
 -- subquery needed to be implemented as a SubPlan node, typically as a