Working version of the code from @roflman79.
/**
* Exclude current post/page from relationship field results
*/
// 1. Add the name=[NAME_OF_RELATIONSHIP_FIELD].
add_filter('acf/fields/relationship/query/name=[NAME_OF_REALTIONSHIP_FIELD]', 'exclude_id', 10, 3);
// 2. Add the $field and $post arguments.
function exclude_id ( $args, $field, $post ) {
//3. $post argument passed in from the query hook is the $post->ID.
$args['post__not_in'] = array( $post );
return $args;
}