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(){
// ...
}
})