The crash happened at 2.10am on Burdyke Avenue in Clifton when a Yamaha motorcycle collided with a stationary Ford Fiesta and a couple walking with their baby.
North Yorkshire Police said: "The rider and pillion passenger of the motorcycle, both men, sustained serious injuries and were taken to hospital.
"The pedestrians, a man, woman and their baby, sustained facial injuries in the incident and were also taken to hospital.
"None of the casualties are believed to have life-threatening injuries.
"The road was closed to allow emergency services to attend to the casualties and to allow officers to examine the scene and recover the vehicles involved.
"Witnesses, including anyone who saw a dark-coloured motorcycle travelling in the area prior to the collision, or anyone with any other information that could assist the collision investigation, is urged to contact North Yorkshire Police on 101, select option 1, and speak to the Force Control Room.
"Please quote reference NYP-12052022-0033 when providing details."