JP was operated on by surgeon Gordon MacKay at Ross Hall Hospital in Glasgow yesterday.
Glasgow Warriors’ team doctor Gerry Haggerty said: "Jonny had his shoulder put back into place at Glasgow's Western Infirmary on Friday night and yesterday he had surgery to tighten up the capsule. The surgeon, Gordon MacKay, was very happy with the repair."
JP was carried off during the first-half of Glasgow's stormy defeat after an altercation with opposing prop Rhys Thomas.
Referee George Clancy yellow-carded Thomas for his part in the incident.