Souare was involved in a two-car collision on Sunday and was rescued by firemen who had to cut the roof off his car.
Palace boss Alan Pardew believes that the defender may face a lengthy spell on the sidelines, but says the outcome could have been a lot worse for Souare.
"He's not in a good way in terms of football, I think he's broken his leg so maybe not so good," he told Sky Sports.
"But thankfully he looks sound other than that, just a bit bashed up.
"We’ll have to look after him and get him back as quickly as we can because he’s a great lad and it’s a big loss. It is a blow but, more importantly, it’s not as bad as it could have been".
Here is an image of the defender's car after he was rescued by firemen.
Our thoughts go out to Papa Souare who was involved in a horrific car accident #CPFC pic.twitter.com/jb0bxB719v
— Crystal Palace News (@CpfcNews_) September 12, 2016