diff --git a/extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryTestMSQ.java b/extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryMSQTest.java
similarity index 81%
rename from extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryTestMSQ.java
rename to extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryMSQTest.java
index 9d31d4f2062..1f45b6ca160 100644
--- a/extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryTestMSQ.java
+++ b/extensions-core/multi-stage-query/src/test/java/org/apache/druid/msq/test/CalciteSelectQueryMSQTest.java
@@ -20,9 +20,11 @@
 package org.apache.druid.msq.test;
 
 import com.fasterxml.jackson.databind.ObjectMapper;
+import com.google.common.collect.ImmutableList;
 import com.google.inject.Injector;
 import com.google.inject.Module;
 import org.apache.druid.guice.DruidInjectorBuilder;
+import org.apache.druid.java.util.common.ISE;
 import org.apache.druid.msq.exec.WorkerMemoryParameters;
 import org.apache.druid.msq.sql.MSQTaskSqlEngine;
 import org.apache.druid.query.groupby.TestGroupByBuffers;
@@ -31,13 +33,15 @@ import org.apache.druid.sql.calcite.CalciteQueryTest;
 import org.apache.druid.sql.calcite.QueryTestBuilder;
 import org.apache.druid.sql.calcite.run.SqlEngine;
 import org.junit.After;
+import org.junit.Assert;
 import org.junit.Before;
 import org.junit.Ignore;
+import org.junit.Test;
 
 /**
  * Runs {@link CalciteQueryTest} but with MSQ engine
  */
-public class CalciteSelectQueryTestMSQ extends CalciteQueryTest
+public class CalciteSelectQueryMSQTest extends CalciteQueryTest
 {
   private TestGroupByBuffers groupByBuffers;
 
@@ -160,4 +164,23 @@ public class CalciteSelectQueryTestMSQ extends CalciteQueryTest
 
   }
 
+  /**
+   * Same query as {@link CalciteQueryTest#testArrayAggQueryOnComplexDatatypes}. ARRAY_AGG is not supported in MSQ currently.
+   * Once support is added, this test can be removed and msqCompatible() can be added to the one in CalciteQueryTest.
+   */
+  @Test
+  @Override
+  public void testArrayAggQueryOnComplexDatatypes()
+  {
+    msqCompatible();
+    try {
+      testQuery("SELECT ARRAY_AGG(unique_dim1) FROM druid.foo", ImmutableList.of(), ImmutableList.of());
+      Assert.fail("query execution should fail");
+    }
+    catch (ISE e) {
+      Assert.assertTrue(
+          e.getMessage().contains("Cannot handle column [a0] with type [ARRAY<COMPLEX<hyperUnique>>]")
+      );
+    }
+  }
 }
diff --git a/sql/src/test/java/org/apache/druid/sql/calcite/CalciteQueryTest.java b/sql/src/test/java/org/apache/druid/sql/calcite/CalciteQueryTest.java
index 88df7939340..78e2e50f3b7 100644
--- a/sql/src/test/java/org/apache/druid/sql/calcite/CalciteQueryTest.java
+++ b/sql/src/test/java/org/apache/druid/sql/calcite/CalciteQueryTest.java
@@ -3550,7 +3550,8 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
   @Test
   public void testNullDoubleTopN()
   {
-    msqCompatible();
+    // Disabled test in MSQ till https://github.com/apache/druid/issues/13951 is resolved
+    // msqCompatible();
     List<Object[]> expected;
     if (useDefault) {
       expected = ImmutableList.of(
@@ -3591,7 +3592,8 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
   @Test
   public void testNullFloatTopN()
   {
-    msqCompatible();
+    // Disabled test in MSQ till https://github.com/apache/druid/issues/13951 is resolved
+    // msqCompatible();
     List<Object[]> expected;
     if (useDefault) {
       expected = ImmutableList.of(
@@ -3632,7 +3634,8 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
   @Test
   public void testNullLongTopN()
   {
-    msqCompatible();
+    // Disabled test in MSQ till https://github.com/apache/druid/issues/13951 is resolved
+    // msqCompatible();
     List<Object[]> expected;
     if (useDefault) {
       expected = ImmutableList.of(
@@ -5698,6 +5701,11 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
     );
   }
 
+  /**
+   * Same query as {@link org.apache.druid.msq.test.CalciteSelectQueryMSQTest#testArrayAggQueryOnComplexDatatypes()}.
+   * ARRAY_AGG is not supported in MSQ currently, but is supported as sql-native. Once support is added,
+   * the overriding test can be removed and msqCompatible() can be added here instead.
+   */
   @Test
   public void testArrayAggQueryOnComplexDatatypes()
   {
@@ -6607,7 +6615,8 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
   {
     // When HLL is disabled, APPROX_COUNT_DISTINCT is still approximate.
 
-    msqCompatible();
+    // Disabled test in MSQ till https://github.com/apache/druid/issues/13950 is resolved
+    // msqCompatible();
     testQuery(
         PLANNER_CONFIG_NO_HLL,
         "SELECT APPROX_COUNT_DISTINCT(dim2) FROM druid.foo",
@@ -6640,7 +6649,8 @@ public class CalciteQueryTest extends BaseCalciteQueryTest
   @Test
   public void testApproxCountDistinctBuiltin()
   {
-    msqCompatible();
+    // Disabled test in MSQ till https://github.com/apache/druid/issues/13950 is resolved
+    // msqCompatible();
     testQuery(
         "SELECT APPROX_COUNT_DISTINCT_BUILTIN(dim2) FROM druid.foo",
         ImmutableList.of(