add_filter( 'getarchives_where', 'customarchives_where' );
add_filter( 'getarchives_join', 'customarchives_join' );

function customarchives_join( $x ) {

global $wpdb;

return $x . " INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id) INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)";

}

function customarchives_where( $x ) {

global $wpdb;

$exclude = '4'; // category id to exclude
return $x . " AND $wpdb->term_taxonomy.taxonomy = 'category' AND $wpdb->term_taxonomy.term_id NOT IN ($exclude)";

}