It can be as long as 6-9 week for soft tissue injuries to repair , in the mean time i would confine him to one small room and strict rest untill this period or you start to see a improvement.
It can be very difficult to rest a cat but you have to be evil to be kind with situations like this. If he shows sighs of worsening or no improvemnet after this time or during then he must be admitted for radiographs of the limp to rule out orthopaedic problems.
Please just rest him , and if he will let you you can try applying ice compress on the damaged area NO LONGER THAN !) MINUTES wrapped in a tea towel to prevent ice burns. Try to do this twice a day and this will help with the pain and a speedier recovery
Hope this helps