The club said that Chris Annakin, Danny Kirmond, and Richard Owen were involved in the incident.
None of the injuries are said to be life threatening.
The accident was said to have happened in the Heath Common Area, near Wakefield at 4pm on Friday, August 26.
The Wakefield Wildcats said in a statement: “The club are aware of a road traffic accident that occurred at approximately 4pm in the Heath Common area yesterday.
“Three players, Chris Annakin, Danny Kirmond, and Richard Owen were involved in the accident, and all remained overnight in hospital with various injuries, although none are life threatening.
“Police and ambulance staff attended the scene, and the club are liaising with them to ascertain exactly what occurred.
“We hope everyone will wish the players a speedy recovery and respect their privacy at this time.
“There will be further information released as and when appropriate.”
West Yorkshire Police said they received a call reporting that a black Subaru Forester estate appeared to have been in collision with a tree on Black Road in Heath.
A force spokesman said: “A 26-year-old male suffered a neck injury and was taken to hospital, a 30-year-old male also attended hospital for cuts to his arms and legs and a 25-year-old male was later found to have suffered a dislocated hip.”
Police are appealing for witnesses to the collision, including a cyclist who is believed to have been on the road at the time.