diff --git a/lib/deploy/stepFunctions/compileIamRole.js b/lib/deploy/stepFunctions/compileIamRole.js
index f1d0ba8c..f99c8d2a 100644
--- a/lib/deploy/stepFunctions/compileIamRole.js
+++ b/lib/deploy/stepFunctions/compileIamRole.js
@@ -35,12 +35,18 @@ function sqsQueueUrlToArn(serverless, queueUrl) {
     const accountId = match[2];
     const queueName = match[3];
     return `arn:aws:sqs:${region}:${accountId}:${queueName}`;
-  } if (isIntrinsic(queueUrl) && queueUrl.Ref) {
-    // most likely we'll see a { Ref: LogicalId }, which we need to map to
-    // { Fn::GetAtt: [ LogicalId, Arn ] } to get the ARN
-    return {
-      'Fn::GetAtt': [queueUrl.Ref, 'Arn'],
-    };
+  }
+  if (isIntrinsic(queueUrl)) {
+    if (queueUrl.Ref) {
+      // most likely we'll see a { Ref: LogicalId }, which we need to map to
+      // { Fn::GetAtt: [ LogicalId, Arn ] } to get the ARN
+      return {
+        'Fn::GetAtt': [queueUrl.Ref, 'Arn'],
+      };
+    }
+    // in case of for example { Fn::ImportValue: sharedValueToImport }
+    // we need to use "*" as ARN
+    return '*';
   }
   serverless.cli.consoleLog(`Unable to parse SQS queue url [${queueUrl}]`);
   return [];
diff --git a/lib/deploy/stepFunctions/compileIamRole.test.js b/lib/deploy/stepFunctions/compileIamRole.test.js
index 8276b971..4437d9ab 100644
--- a/lib/deploy/stepFunctions/compileIamRole.test.js
+++ b/lib/deploy/stepFunctions/compileIamRole.test.js
@@ -362,6 +362,56 @@ describe('#compileIamRole', () => {
     expect(policy.PolicyDocument.Statement[0].Resource).to.equal('*');
   });
 
+  it('should give sqs:SendMessage permission to * whenever QueueUrl is some intrinsic function except Ref', () => {
+    const helloQueue = 'https://sqs.#{AWS::Region}.amazonaws.com/#{AWS::AccountId}/hello';
+    const worldQueue = 'https://sqs.us-east-1.amazonaws.com/#{AWS::AccountId}/world';
+
+    const genStateMachine = (name, queueUrl) => ({
+      name,
+      definition: {
+        StartAt: 'A',
+        States: {
+          A: {
+            Type: 'Task',
+            Resource: 'arn:aws:states:::sqs:sendMessage',
+            Parameters: {
+              QueueUrl: queueUrl,
+              Message: '42',
+            },
+            Next: 'B',
+          },
+          B: {
+            Type: 'Task',
+            Resource: 'arn:aws:states:::sqs:sendMessage',
+            Parameters: {
+              QueueUrl: {
+                'Fn::ImportValue': 'some-shared-value-here',
+              },
+              Message: '42',
+            },
+            End: true,
+          },
+        },
+      },
+    });
+
+    serverless.service.stepFunctions = {
+      stateMachines: {
+        myStateMachine1: genStateMachine('stateMachineBeta1', helloQueue),
+        myStateMachine2: genStateMachine('stateMachineBeta2', worldQueue),
+      },
+    };
+
+    serverlessStepFunctions.compileIamRole();
+    const policy = serverlessStepFunctions.serverless.service
+      .provider.compiledCloudFormationTemplate.Resources.IamRoleStateMachineExecution
+      .Properties.Policies[0];
+
+    // when using instrinct functions other than Ref to define QueueUrl
+    // we can't recontruct ARN from it, so we need to give broad permissions
+    expect(policy.PolicyDocument.Statement[0].Resource).to.equal('*');
+  });
+
   it('should not give sqs:SendMessage permission if QueueUrl and QueueUrl.$ are missing', () => {
     const genStateMachine = name => ({
       name,