diff --git a/mlir/lib/Target/LLVMIR/ModuleImport.cpp b/mlir/lib/Target/LLVMIR/ModuleImport.cpp
--- a/mlir/lib/Target/LLVMIR/ModuleImport.cpp
+++ b/mlir/lib/Target/LLVMIR/ModuleImport.cpp
@@ -1062,6 +1062,11 @@
     return root;
   }
 
+  if (isa<llvm::BlockAddress>(constant)) {
+    return emitError(loc)
+           << "blockaddress is not implemented in the LLVM dialect";
+  }
+
   return emitError(loc) << "unhandled constant: " << diag(*constant);
 }
 
diff --git a/mlir/test/Target/LLVMIR/Import/import-failure.ll b/mlir/test/Target/LLVMIR/Import/import-failure.ll
--- a/mlir/test/Target/LLVMIR/Import/import-failure.ll
+++ b/mlir/test/Target/LLVMIR/Import/import-failure.ll
@@ -22,7 +22,7 @@
 ; // -----
 
 ; CHECK:      import-failure.ll
-; CHECK-SAME: error: unhandled constant: ptr blockaddress(@unhandled_constant, %bb1)
+; CHECK-SAME: error: blockaddress is not implemented in the LLVM dialect
 ; CHECK:      import-failure.ll
 ; CHECK-SAME: error: unhandled instruction: ret ptr blockaddress(@unhandled_constant, %bb1)
 define ptr @unhandled_constant() {
@@ -33,7 +33,7 @@
 ; // -----
 
 ; CHECK:      import-failure.ll
-; CHECK-SAME: error: unhandled constant: ptr blockaddress(@unhandled_global, %bb1)
+; CHECK-SAME: error: blockaddress is not implemented in the LLVM dialect
 ; CHECK:      import-failure.ll
 ; CHECK-SAME: error: unhandled global variable: @private = private global ptr blockaddress(@unhandled_global, %bb1)
 @private = private global ptr blockaddress(@unhandled_global, %bb1)