Wakefield Wildcats player Chris Annakin dislocated his hip and team-mate Richard Owen suffered a neck injury when their car hit a tree on Friday.
Captain Danny Kirmond, 30, was also in the car and received cuts to his arms and legs, according to police.
The trio were kept in hospital overnight after the single-vehicle collision happened at 15:46 BST on Black Road in Wakefield.
The club said further information would be released "as and when appropriate".
Wakefield have no fixture this weekend because of the Challenge Cup final and are next in action at Castleford on Friday, 2 September.
Police are appealing for any witnesses to the incident to phone 101.
A club statement said: "Wakefield 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."