Some people like the celebrations, others just want to get on with the business of the day, and there are those that don't like being the center of attention on their birthday. I would suggest finding out how much this student likes to celebrate on their birthday, and from that decide what to do. You wouldn't want to do something that is upsetting to your student.
If they want to keep it low key, you do something like have them choose a fun piece to study.