The left-back injured his thigh and jaw bone in the two-car collision between junctions three and four on the motorway, the Premier League club confirmed.
He had to be cut free from the car by firefighters, before being airlifted to hospital.
Crystal Palace said he would remain in hospital whilst he receives treatment.
"The club are liaising closely with the hospital on his progress and we obviously wish him a speedy recovery. Our thoughts are with Pape and his family at this time," added the club.
Supporters had questioned the player's whereabouts after he was not included in the team's squad at Middlesbrough on Saturday.
One unofficial fans' twitter account said Souare had been airlifted to hospital, and another Twitter user said he thought the player had broken a leg.
Emergency services were called on Sunday shortly before 12.10pm to reports of two cars in collision on the eastbound carriageway of the M4, between junctions four and three.
Police said the driver of one of the cars, described as a man in his 20s, was taken to an east London hospital for treatment. They said his injuries were not life-threatening.
The driver of the other car did not require hospital treatment.
Officers from the Serious Collision Investigation Unit are appealing for anyone who witnessed the collision, or the events leading up to it, to call them on 020 8543 5157.
Police said enquiries were ongoing, and no one is believed to have been arrested.
The London Fire Brigade said crews had to cut a man free from one of the vehicles before he could be taken to hospital by London's Air Ambulance.
It said five fire engines and a fire and rescue unit from Feltham, Hayes and Heathrow fire stations attended the incident.
There were still long delays on the M4 on Monday (September 12) morning, between junctions three and six, with one lane closed near junction three at Hayes.
The Highways Agency said the disruption was due to ongoing barrier repair work and to a further crash that morning between junctions five and four B near Slough.
It advised drivers heading into London on Monday and those on the M25 heading for the M4 or Heathrow Airport to consider alternative routes.
Another crash on the A406 North Circular Road at Chiswick Roundabout, close to the M4, was also causing disruption on Monday morning.
Police said they were called to a collision involving a lorry and a pick up truck, but nobody had been injured.
One lane was blocked southbound and there were tailbacks to Ealing Common.