diff --git a/sdk/core/azure-core/inc/azure/core/uuid.hpp b/sdk/core/azure-core/inc/azure/core/uuid.hpp
index 756aa60a2..673bdaf2c 100644
--- a/sdk/core/azure-core/inc/azure/core/uuid.hpp
+++ b/sdk/core/azure-core/inc/azure/core/uuid.hpp
@@ -79,12 +79,15 @@ namespace Azure { namespace Core {
      */
     constexpr bool operator==(Uuid const& other) const
     {
-      // std::array::operator==() is not a constexpr until C++20
-      for (size_t i = 0; i < m_uuid.size(); ++i)
+      if (this != &other)
       {
-        if (m_uuid[i] != other.m_uuid[i])
+        // std::array::operator==() is not a constexpr until C++20
+        for (size_t i = 0; i < m_uuid.size(); ++i)
         {
-          return false;
+          if (m_uuid[i] != other.m_uuid[i])
+          {
+            return false;
+          }
         }
       }
 
diff --git a/sdk/core/azure-core/test/ut/uuid_test.cpp b/sdk/core/azure-core/test/ut/uuid_test.cpp
index 239725e21..162472c2f 100644
--- a/sdk/core/azure-core/test/ut/uuid_test.cpp
+++ b/sdk/core/azure-core/test/ut/uuid_test.cpp
@@ -205,3 +205,60 @@ TEST(Uuid, parse)
   // Just a string of text
   ASSERT_THROW(Uuid::Parse("The quick brown fox jumps over the lazy dog."), std::invalid_argument);
 }
+
+TEST(Uuid, equality)
+{
+  {
+    Uuid const a;
+    EXPECT_TRUE(a == a);
+    EXPECT_FALSE(a != a);
+  }
+
+  {
+    Uuid const a = Uuid::Parse("00000000-0000-0000-0000-000000000000");
+    EXPECT_TRUE(a == a);
+    EXPECT_FALSE(a != a);
+  }
+
+  {
+    Uuid const a = Uuid::Parse("00112233-4455-6677-8899-aabbccddeeff");
+    EXPECT_TRUE(a == a);
+    EXPECT_FALSE(a != a);
+  }
+
+  {
+    Uuid const a;
+    Uuid const b;
+    EXPECT_TRUE(a == b);
+    EXPECT_TRUE(b == a);
+    EXPECT_FALSE(a != b);
+    EXPECT_FALSE(b != a);
+  }
+
+  {
+    Uuid const a;
+    Uuid const b = Uuid::Parse("00000000-0000-0000-0000-000000000000");
+    EXPECT_TRUE(a == b);
+    EXPECT_TRUE(b == a);
+    EXPECT_FALSE(a != b);
+    EXPECT_FALSE(b != a);
+  }
+
+  {
+    Uuid const a;
+    Uuid const b = Uuid::Parse("00112233-4455-6677-8899-aabbccddeeff");
+    EXPECT_FALSE(a == b);
+    EXPECT_FALSE(b == a);
+    EXPECT_TRUE(a != b);
+    EXPECT_TRUE(b != a);
+  }
+
+  {
+    Uuid const a = Uuid::Parse("ffeeddcc-bbaa-9988-7766-554433221100");
+    Uuid const b = Uuid::Parse("00112233-4455-6677-8899-aabbccddeeff");
+    EXPECT_FALSE(a == b);
+    EXPECT_FALSE(b == a);
+    EXPECT_TRUE(a != b);
+    EXPECT_TRUE(b != a);
+  }
+}