If your Node.js app is an azure web or Azure Webjob, you could start it with REST API. Here are web app and webjob.
From your situation, I think you could just develop a queue trigger Function(Node.js), don't have to use a queue trigger function to call Node.js app.The below is a Node.js queue Function sample.
module.exports = async function (context, message) {
context.log('Node.js queue trigger function processed work item', message);
// OR access using context.bindings.<name>
// context.log('Node.js queue trigger function processed work item', context.bindings.myQueueItem);
context.log('expirationTime =', context.bindingData.expirationTime);
context.log('insertionTime =', context.bindingData.insertionTime);
context.log('nextVisibleTime =', context.bindingData.nextVisibleTime);
context.log('id =', context.bindingData.id);
context.log('popReceipt =', context.bindingData.popReceipt);
context.log('dequeueCount =', context.bindingData.dequeueCount);
context.done();
};
Further more information about Node.js Function, you could refer to these docs:Trigger - JavaScript example and Azure Functions JavaScript developer guide.