diff --git a/clang-tools-extra/clang-tidy/performance/MoveConstArgCheck.cpp b/clang-tools-extra/clang-tidy/performance/MoveConstArgCheck.cpp
--- a/clang-tools-extra/clang-tidy/performance/MoveConstArgCheck.cpp
+++ b/clang-tools-extra/clang-tidy/performance/MoveConstArgCheck.cpp
@@ -103,6 +103,7 @@
     AlreadyCheckedMoves.insert(CallMove);
 
   const Expr *Arg = CallMove->getArg(0);
+  const QualType ArgType = Arg->getType();
   SourceManager &SM = Result.Context->getSourceManager();
 
   CharSourceRange MoveRange =
@@ -112,12 +113,11 @@
   if (!FileMoveRange.isValid())
     return;
 
-  bool IsConstArg = Arg->getType().isConstQualified();
-  bool IsTriviallyCopyable =
-      Arg->getType().isTriviallyCopyableType(*Result.Context);
+  bool IsConstArg = ArgType.isConstQualified();
+  bool IsTriviallyCopyable = ArgType.isTriviallyCopyableType(*Result.Context);
 
   if (IsConstArg || IsTriviallyCopyable) {
-    if (const CXXRecordDecl *R = Arg->getType()->getAsCXXRecordDecl()) {
+    if (const CXXRecordDecl *R = ArgType->getAsCXXRecordDecl()) {
       // According to [expr.prim.lambda]p3, "whether the closure type is
       // trivially copyable" property can be changed by the implementation of
       // the language, so we shouldn't rely on it when issuing diagnostics.
@@ -151,7 +151,7 @@
                   << IsConstArg << IsVariable << IsTriviallyCopyable
                   << IsRVRefParam
                   << (IsConstArg && IsVariable && !IsTriviallyCopyable) << Var
-                  << Arg->getType();
+                  << ArgType;
       if (!IsRVRefParam)
         replaceCallWithArg(CallMove, Diag, SM, getLangOpts());
     }
@@ -196,11 +196,19 @@
     if ((*InvocationParmType)->isRValueReferenceType())
       return;
 
-    auto Diag = diag(FileMoveRange.getBegin(),
-                     "passing result of std::move() as a const reference "
-                     "argument; no move will actually happen");
+    {
+      auto Diag = diag(FileMoveRange.getBegin(),
+                       "passing result of std::move() as a const reference "
+                       "argument; no move will actually happen");
+
+      replaceCallWithArg(CallMove, Diag, SM, getLangOpts());
+    }
 
-    replaceCallWithArg(CallMove, Diag, SM, getLangOpts());
+    if (const CXXRecordDecl *RecordDecl = ArgType->getAsCXXRecordDecl();
+        !RecordDecl->hasMoveConstructor() || !RecordDecl->hasMoveAssignment())
+      diag(RecordDecl->getSourceRange().getBegin(),
+           "'%0' is not move constructible", DiagnosticIDs::Note)
+          << RecordDecl->getName();
   }
 }
 
diff --git a/clang-tools-extra/docs/ReleaseNotes.rst b/clang-tools-extra/docs/ReleaseNotes.rst
--- a/clang-tools-extra/docs/ReleaseNotes.rst
+++ b/clang-tools-extra/docs/ReleaseNotes.rst
@@ -374,6 +374,10 @@
   `IgnoreTemplateInstantiations` option to optionally ignore virtual function
   overrides that are part of template instantiations.
 
+- Improved :doc:`performance-move-const-arg
+  <clang-tidy/checks/performance/move-const-arg>`: warning when no move
+  constructor is available.
+
 - Improved :doc:`performance-no-automatic-move
   <clang-tidy/checks/performance/no-automatic-move>`: warn on ``const &&``
   constructors.
diff --git a/clang-tools-extra/test/clang-tidy/checkers/performance/move-const-arg.cpp b/clang-tools-extra/test/clang-tidy/checkers/performance/move-const-arg.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/performance/move-const-arg.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/performance/move-const-arg.cpp
@@ -340,3 +340,51 @@
   // CHECK-FIXES: choice(a, std::move(a));
   // CHECK-MESSAGES: :[[@LINE-3]]:24: warning: std::move of the variable 'a' of the trivially-copyable type 'int' has no effect [performance-move-const-arg]
 }
+
+namespace issue_62550 {
+
+struct NonMoveConstructable {
+  NonMoveConstructable();
+  NonMoveConstructable(const NonMoveConstructable&);
+  NonMoveConstructable& operator=(const NonMoveConstructable&);
+  NonMoveConstructable& operator=(NonMoveConstructable&&);
+};
+
+void testNonMoveConstructible() {
+  NonMoveConstructable t1;
+  NonMoveConstructable t2{std::move(t1)};
+  // CHECK-MESSAGES: :[[@LINE-1]]:27: warning: passing result of std::move() as a const reference argument; no move will actually happen [performance-move-const-arg]
+}
+
+struct NonMoveAssignable {
+  NonMoveAssignable();
+  NonMoveAssignable(const NonMoveAssignable&);
+  NonMoveAssignable(NonMoveAssignable&&);
+
+  NonMoveAssignable& operator=(const NonMoveAssignable&);
+};
+
+void testNonMoveAssignable() {
+  NonMoveAssignable t1;
+  NonMoveAssignable t2;
+
+  t2 = std::move(t1);
+  // CHECK-MESSAGES: :[[@LINE-1]]:8: warning: passing result of std::move() as a const reference argument; no move will actually happen [performance-move-const-arg]
+}
+
+struct NonMoveable {
+  NonMoveable();
+  NonMoveable(const NonMoveable&);
+  NonMoveable& operator=(const NonMoveable&);
+};
+
+void testNonMoveable() {
+  NonMoveable t1;
+  NonMoveable t2{std::move(t1)};
+  // CHECK-MESSAGES: :[[@LINE-1]]:18: warning: passing result of std::move() as a const reference argument; no move will actually happen [performance-move-const-arg]
+
+  t1 = std::move(t2);
+  // CHECK-MESSAGES: :[[@LINE-1]]:8: warning: passing result of std::move() as a const reference argument; no move will actually happen [performance-move-const-arg]
+}
+
+} // namespace issue_62550