You can use getarchives_where
hook of wp_get_archives() function
Add this function to your functions.php:
function Cpt_getarchives_where_filter( $where , $r ) {
$post_type="blog";
return str_replace( "post_type="post"" , "post_type="$post_type"" , $where );
}
Then when you want your monthly archive put this:
add_filter( 'getarchives_where' , 'Cpt_getarchives_where_filter' , 10 , 2 );
wp_get_archives();
remove_filter('getarchives_where' , 'Cpt_getarchives_where_filter' , 10 );