action.js

export function handleAction (action) {
  const args = action.payload || []
  switch (action.type) {
    case DO_SOMETHING:
      return doSomething(...args)
    default:
      break
  }
}

function doSomething () {
  // ...
}

middleware.js

export default function workerActions (store) {
  const worker = new window.Worker('/worker.js')

  worker.addEventListener('message', ({ data: action }) => {
    store.dispatch(action)
  })

  return next => action => {
    worker.postMessage(action)
    return next(action)
  }
}

worker.js

import { createStore, applyMiddleware } from 'redux'

import { handleAction } from './action'
import reducer from './reducer'

const middleware = store => next => action => {
  self.postMessage(action)
  return next(action)
}
const store = createStore(reducer, applyMiddleware(middleware))

let promise = Promise.resolve()
self.addEventListener('message', event => {
  promise = promise.then(() => {
    return store.dispatch(handleAction(event.data))
  })
})