diff --git a/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp b/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
--- a/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
+++ b/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
@@ -83,15 +83,19 @@
   // variable being declared. The assumption is that the const reference being
   // returned either points to a global static variable or to a member of the
   // called object.
-  return cxxMemberCallExpr(
-      callee(cxxMethodDecl(
-                 returns(hasCanonicalType(matchers::isReferenceToConst())))
-                 .bind(MethodDeclId)),
-      on(declRefExpr(to(
-          varDecl(
-              unless(hasType(qualType(hasCanonicalType(hasDeclaration(namedDecl(
-                  matchers::matchesAnyListedName(ExcludedContainerTypes))))))))
-              .bind(ObjectArgId)))));
+  const auto MethodDecl =
+      cxxMethodDecl(returns(hasCanonicalType(matchers::isReferenceToConst())))
+          .bind(MethodDeclId);
+  const auto ReceiverExpr = declRefExpr(to(varDecl().bind(ObjectArgId)));
+  const auto ReceiverTypeDecl =
+      namedDecl(unless(matchers::matchesAnyListedName(ExcludedContainerTypes)));
+
+  return expr(anyOf(
+      cxxMemberCallExpr(callee(MethodDecl), on(ReceiverExpr),
+                        thisPointerType(ReceiverTypeDecl)),
+      cxxOperatorCallExpr(callee(MethodDecl), hasArgument(0, ReceiverExpr),
+                          hasArgument(0, hasType(recordType(hasDeclaration(
+                                             ReceiverTypeDecl)))))));
 }
 
 AST_MATCHER_FUNCTION(StatementMatcher, isConstRefReturningFunctionCall) {
diff --git a/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp b/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
@@ -24,6 +24,11 @@
   operator int() const; // Implicit conversion to int.
 };
 
+struct ExpensiveToCopyContainer {
+  const ExpensiveToCopyType &operator[](int) const;
+  const ExpensiveToCopyType &operator[](int);
+};
+
 struct TrivialToCopyType {
   const TrivialToCopyType &reference() const;
 };
@@ -138,6 +143,50 @@
   VarCopyConstructed.constMethod();
 }
 
+void PositiveOperatorCallConstReferenceParam(const ExpensiveToCopyContainer &C) {
+  const auto AutoAssigned = C[42];
+  // CHECK-MESSAGES: [[@LINE-1]]:14: warning: the const qualified variable 'AutoAssigned'
+  // CHECK-FIXES: const auto& AutoAssigned = C[42];
+  AutoAssigned.constMethod();
+
+  const auto AutoCopyConstructed(C[42]);
+  // CHECK-MESSAGES: [[@LINE-1]]:14: warning: the const qualified variable 'AutoCopyConstructed'
+  // CHECK-FIXES: const auto& AutoCopyConstructed(C[42]);
+  AutoCopyConstructed.constMethod();
+
+  const ExpensiveToCopyType VarAssigned = C[42];
+  // CHECK-MESSAGES: [[@LINE-1]]:29: warning: the const qualified variable 'VarAssigned'
+  // CHECK-FIXES: const ExpensiveToCopyType& VarAssigned = C[42];
+  VarAssigned.constMethod();
+
+  const ExpensiveToCopyType VarCopyConstructed(C[42]);
+  // CHECK-MESSAGES: [[@LINE-1]]:29: warning: the const qualified variable 'VarCopyConstructed'
+  // CHECK-FIXES: const ExpensiveToCopyType& VarCopyConstructed(C[42]);
+  VarCopyConstructed.constMethod();
+}
+
+void PositiveOperatorCallConstValueParam(const ExpensiveToCopyContainer C) {
+  const auto AutoAssigned = C[42];
+  // CHECK-MESSAGES: [[@LINE-1]]:14: warning: the const qualified variable 'AutoAssigned'
+  // CHECK-FIXES: const auto& AutoAssigned = C[42];
+  AutoAssigned.constMethod();
+
+  const auto AutoCopyConstructed(C[42]);
+  // CHECK-MESSAGES: [[@LINE-1]]:14: warning: the const qualified variable 'AutoCopyConstructed'
+  // CHECK-FIXES: const auto& AutoCopyConstructed(C[42]);
+  AutoCopyConstructed.constMethod();
+
+  const ExpensiveToCopyType VarAssigned = C[42];
+  // CHECK-MESSAGES: [[@LINE-1]]:29: warning: the const qualified variable 'VarAssigned'
+  // CHECK-FIXES: const ExpensiveToCopyType& VarAssigned = C[42];
+  VarAssigned.constMethod();
+
+  const ExpensiveToCopyType VarCopyConstructed(C[42]);
+  // CHECK-MESSAGES: [[@LINE-1]]:29: warning: the const qualified variable 'VarCopyConstructed'
+  // CHECK-FIXES: const ExpensiveToCopyType& VarCopyConstructed(C[42]);
+  VarCopyConstructed.constMethod();
+}
+
 void PositiveLocalConstValue() {
   const ExpensiveToCopyType Obj;
   const auto UnnecessaryCopy = Obj.reference();