She's only ever done a concert on her birthday once! Back in 2006 on the Confessions Tour, an eighth and final UK show for August 16th at Wembley Arena in London was added long after the initial dates had sold out.
Madonna-TV was there to film exclusively as the concert audience sang "Happy Birthday" during a break in the show. Madonna thanked everyone and gave a little speech.
After the show, madonna-tv viewers were filmed giving their birthday wishes to Madonna! Watch out for an appearance by the legendary Pud Whacker amongst others.
(Madonna-TV, August 2006)