How to exclude post from being queried based on custom meta value

According to the codex for WP_Query, you should be able to tack on some meta related arguments to your args array (this is untested):

$review_args = array(
    'orderby' => 'post_date',
    'order' => 'ASC',
    'posts_per_page' => '1',
    'cat' => 22,
    'meta_query' => array(
                        'key'=>'reviewed_by',
                        'value'=> $reviewed_by_array,
                        'compare'=> 'NOT IN'
                    )
);

$review_query = new WP_Query($review_args);