The accident happened in the Heath Common area, which is close to Trinity’s Belle Vue ground.
Wakefield have no game this weekend, but visit Castleford Tigers on Friday, September 2.
A club statement said: “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.”