JButton button = new JButton("Start");
button.addActionListener(new ActionListener() {
  @Override
  public void actionPerformed(ActionEvent evt) {
    Thread t = new Thread(new Runnable() {
      @Override
      public void run() {
        menu.setEnabled(false);

        MySwingWorker worker = new MySwingWorker();
        worker.execute();

        while (true) {
          if (worker.isCancelled() || worker.isDone()) {
            menu.setEnabled(true);
            break;
          }
        }
      }
    });
    t.start();
  }
});