While displaying the messager dialog, assign a custom class to hide the dialog button. Please refer to the code below.
<style type="text/css">
  .mymessager .dialog-button{
    display: none;
  }
</style>
$.messager.alert({
  title: 'My Title',
  msg: 'The alert message.',
  cls: 'mymessager',
  fn: function(){
    // ...
  }
})