There are two questions here:
- Is it possible to play tabla to the point of injury?
- What kind of injuries can occur when playing tabla?
The answer to the first is "yes". The answer to the second, broadly, is that there are any number of injuries that can occur, primarily involving the muscles and nerves of the arms, shoulders, and back.
There are anecdotal reports of tabla-related pain: for example,
I discovered that [poor sitting support] was actually causing additional stress on my shoulders and back, which was leading to pain in my forearm. (SOURCE)
Whenever I play a heavy dose of ti-ra-ki-ta, my forearm and upper arm start hurting. (SOURCE)
NOTE: both of these sources also recommend solutions to their respective problems. These are not medical sites and remedies there should not be understood as medical advice for preventing or resolving pain or injury.
There are also a variety of studies related to tabla playing and pain or injury. These include:
- "The effect of conditioning physiotherapy exercises on tabla playing related wrist pain in young tabla learners: a randomized controlled trial" by Punyaja Jani and Dr. Gauri M Afle. (LINK)
- "Playing-Related Musculoskeletal Disorders Among Indian Tabla Players" by Wricha Mishra, et al. (LINK)
NOTE: It is left to the reader to determine if these studies or any additional studies references by them are from reliable sources.