Water is leaking from upstairs shower. I believe water seeps through broken grout. What is proper way to repair?

Is cracked grout on wall or floor? If floor, then you may have more of a problem then grout crack... may be the shower pan or the shower strainer (get back to us on this)... If wall then...

Remove the grout with a grout removal tool (sold at home supply stores) and then mix up some new grout and patch... let dry.. good to go. Use nonsanded grout for wall joints 1/8" or less... sanded grout would be for larger grout joints.

Also, check behind the shower valve face plate to be sure leak is not coming from the valve itself... look in behind plate (with flashlight) while running shower and just be sure leak is not coming from above shower valve at shower arm connection, etc.

Good luck. Hey, rate the answer if it helped. Thank you.