The 26-year-old was airlifted to hospital after a crash on the M4 motorway.
Chairman Steve Parish told the club website: “Pape Souare has this morning undergone surgery on both his jaw and thigh.
“He is expected to make a full recovery and should be discharged on Friday.”
Parrish added: “We would like to make special mention of the London Air Ambulance service who flew Pape directly from the scene to the hospital, ensuring that he rapidly had access to the very best medical care.”
The Senegalese has made 44 Premier League appearances for the Eagles.