I haven’t found an easy way but here is a solution:
I get the month and year from the current archive and compare them with the text.
$year = get_query_var( 'year' );
$monthnum = get_query_var( 'monthnum' );
$monthname = $GLOBALS['wp_locale']->get_month( $monthnum );
$date = $monthname . ' ' . $year;
if ( $text === $date )
$active_class="class="current-menu-item"";