diff --git a/core/src/main/java/org/apache/calcite/sql/fun/SqlMapValueConstructor.java b/core/src/main/java/org/apache/calcite/sql/fun/SqlMapValueConstructor.java
index 7f3da3bdb23..a4974712006 100644
--- a/core/src/main/java/org/apache/calcite/sql/fun/SqlMapValueConstructor.java
+++ b/core/src/main/java/org/apache/calcite/sql/fun/SqlMapValueConstructor.java
@@ -42,7 +42,8 @@
  */
 public class SqlMapValueConstructor extends SqlMultisetValueConstructor {
   public SqlMapValueConstructor() {
-    super("MAP", SqlKind.MAP_VALUE_CONSTRUCTOR);
+    // no need to deduce NULL operand type
+    super("MAP", SqlKind.MAP_VALUE_CONSTRUCTOR, null);
   }
 
   @SuppressWarnings("argument.type.incompatible")
diff --git a/core/src/main/java/org/apache/calcite/sql/fun/SqlMultisetValueConstructor.java b/core/src/main/java/org/apache/calcite/sql/fun/SqlMultisetValueConstructor.java
index 8efd45a3eb3..acbafc97e01 100644
--- a/core/src/main/java/org/apache/calcite/sql/fun/SqlMultisetValueConstructor.java
+++ b/core/src/main/java/org/apache/calcite/sql/fun/SqlMultisetValueConstructor.java
@@ -28,6 +28,7 @@
 import org.apache.calcite.sql.type.InferTypes;
 import org.apache.calcite.sql.type.OperandTypes;
 import org.apache.calcite.sql.type.ReturnTypes;
+import org.apache.calcite.sql.type.SqlOperandTypeInference;
 import org.apache.calcite.sql.type.SqlTypeUtil;
 
 import org.checkerframework.checker.nullness.qual.Nullable;
@@ -54,12 +55,18 @@ public SqlMultisetValueConstructor() {
   }
 
   protected SqlMultisetValueConstructor(String name, SqlKind kind) {
+    this(name, kind, InferTypes.FIRST_KNOWN);
+  }
+
+  protected SqlMultisetValueConstructor(
+      String name, SqlKind kind,
+      @Nullable SqlOperandTypeInference operandTypeInference) {
     super(
         name,
         kind, MDX_PRECEDENCE,
         false,
         ReturnTypes.ARG0,
-        InferTypes.FIRST_KNOWN,
+        operandTypeInference,
         OperandTypes.VARIADIC);
   }
 
diff --git a/core/src/test/resources/sql/misc.iq b/core/src/test/resources/sql/misc.iq
index 8bdb345b22f..74ee82abb8f 100644
--- a/core/src/test/resources/sql/misc.iq
+++ b/core/src/test/resources/sql/misc.iq
@@ -2602,4 +2602,20 @@ FROM (
 (1 row)
 
 !ok
+
+# [CALCITE-6040] The operand type inference of SqlMapValueConstructor is incorrect
+SELECT
+  map['foo', null],
+  map[null, 'foo'],
+  map[1, 'foo', 2, null],
+  map[1, null, 2, 'foo'];
++------------+------------+-----------------+-----------------+
+| EXPR$0     | EXPR$1     | EXPR$2          | EXPR$3          |
++------------+------------+-----------------+-----------------+
+| {foo=null} | {null=foo} | {1=foo, 2=null} | {1=null, 2=foo} |
++------------+------------+-----------------+-----------------+
+(1 row)
+
+!ok
+
 # End misc.iq
diff --git a/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java b/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
index fd11a31f052..bfc14daab70 100644
--- a/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
+++ b/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
@@ -10442,6 +10442,27 @@ private static void checkArrayConcatAggFuncFails(SqlOperatorFixture t) {
     f.checkScalar("map['washington', 1, 'obama', 44]",
         "{washington=1, obama     =44}",
         "(CHAR(10) NOT NULL, INTEGER NOT NULL) MAP NOT NULL");
+
+    // check null key or null value
+    f.checkScalar("map['foo', null]",
+        "{foo=null}",
+        "(CHAR(3) NOT NULL, NULL) MAP NOT NULL");
+    f.checkScalar("map[null, 'foo']",
+        "{null=foo}",
+        "(NULL, CHAR(3) NOT NULL) MAP NOT NULL");
+    f.checkScalar("map[1, 'foo', 2, null]",
+        "{1=foo, 2=null}",
+        "(INTEGER NOT NULL, CHAR(3)) MAP NOT NULL");
+    f.checkScalar("map[1, null, 2, 'foo']",
+        "{1=null, 2=foo}",
+        "(INTEGER NOT NULL, CHAR(3)) MAP NOT NULL");
+    f.checkScalar("map[1, null, 2, null]",
+        "{1=null, 2=null}",
+        "(INTEGER NOT NULL, NULL) MAP NOT NULL");
+    f.checkScalar("map[null, 1, null, 2]",
+        "{null=2}",
+        "(NULL, INTEGER NOT NULL) MAP NOT NULL");
+
     // elements cast
     f.checkScalar("map['A', 1, 'ABC', 2]", "{A  =1, ABC=2}",
         "(CHAR(3) NOT NULL, INTEGER NOT NULL) MAP NOT NULL");