diff --git a/pkg/sql/alter_table.go b/pkg/sql/alter_table.go
index 632d33259018..3bc72b455e99 100644
--- a/pkg/sql/alter_table.go
+++ b/pkg/sql/alter_table.go
@@ -201,6 +201,12 @@ func (n *alterTableNode) startExec(params runParams) error {
 					continue
 				}
 
+				if d.Predicate != nil {
+					return pgerror.New(pgcode.InvalidTableDefinition,
+						"partial unique constraints cannot be added in ALTER TABLE, "+
+							"use CREATE UNIQUE INDEX instead")
+				}
+
 				if d.PrimaryKey {
 					// We only support "adding" a primary key when we are using the
 					// default rowid primary index or if a DROP PRIMARY KEY statement
diff --git a/pkg/sql/logictest/testdata/logic_test/alter_table b/pkg/sql/logictest/testdata/logic_test/alter_table
index 8767e3b74e50..01eb0dc99033 100644
--- a/pkg/sql/logictest/testdata/logic_test/alter_table
+++ b/pkg/sql/logictest/testdata/logic_test/alter_table
@@ -1481,7 +1481,12 @@ ALTER TABLE unique_without_index ADD COLUMN f INT UNIQUE WITHOUT INDEX
 # constraint.
 statement ok
 ALTER TABLE unique_without_index ADD COLUMN f INT;
-ALTER TABLE unique_without_index ADD CONSTRAINT my_unique_f UNIQUE WITHOUT INDEX (f);
+ALTER TABLE unique_without_index ADD CONSTRAINT my_unique_f UNIQUE WITHOUT INDEX (f)
+
+# Partial predicates are allowed for UNIQUE WITHOUT INDEX, but not UNIQUE.
+# TODO(mgartner): This is confusing, and something we should think more about
+# if we ever make UNIQUE WITHOUT INDEX available by default.
+statement ok
 ALTER TABLE unique_without_index ADD CONSTRAINT my_partial_unique_f UNIQUE WITHOUT INDEX (f) WHERE f > 0
 
 # The unique constraint predicate must be valid. It cannot reference
diff --git a/pkg/sql/logictest/testdata/logic_test/partial_index b/pkg/sql/logictest/testdata/logic_test/partial_index
index a5a6c4260cf3..f904c7df3ad1 100644
--- a/pkg/sql/logictest/testdata/logic_test/partial_index
+++ b/pkg/sql/logictest/testdata/logic_test/partial_index
@@ -76,6 +76,14 @@ CREATE TABLE t4 (a INT, UNIQUE INDEX (a) WHERE a = 0)
 statement error expected index predicate expression to have type bool, but '1' has type int
 CREATE TABLE error (a INT, UNIQUE INDEX (a) WHERE 1)
 
+# Disallow partial unique constraints in ALTER TABLE.
+
+statement ok
+CREATE TABLE up (a INT)
+
+statement error partial unique constraints cannot be added in ALTER TABLE, use CREATE UNIQUE INDEX instead
+ALTER TABLE up ADD CONSTRAINT partial_unique UNIQUE (a) WHERE a > 0
+
 # Validate CREATE INDEX predicate.
 
 statement ok
diff --git a/pkg/sql/parser/sql.y b/pkg/sql/parser/sql.y
index 98a360ae121e..b8f7f969e15b 100644
--- a/pkg/sql/parser/sql.y
+++ b/pkg/sql/parser/sql.y
@@ -6801,6 +6801,9 @@ constraint_elem:
       Expr: $3.expr(),
     }
   }
+// TODO(mgartner): Postgres does not allow partial unique constraints. It only
+// allows partial unique indexes. The opt_where_clause should be removed so that
+// it is a syntax error. See discussion in #65825.
 | UNIQUE opt_without_index '(' index_params ')'
     opt_storing opt_interleave opt_partition_by_index opt_deferrable opt_where_clause
   {