Officers were called to Linton Road by the ambulance service at around 10.30pm last night (September 2), where a man was reported to have stab wounds.
When they got to the scene, two men were found with injuries. They were taken to hospital for treatment, although their injuries are not thought to be life threatening.
Enquiries established the incident took place on Park Lodge Lane, close to the junction with Shepley Street.
A robbery in Lower Warrengate which was reported at 10.52pm is believed to be linked to the incident.
A 29-year-old man has been arrested in connection with both matters and remains in custody.
Further enquiries are being made by Wakefield District CID and anyone who witnessed any suspicious activity in the Park Lodge Lane area around the time of the incident is asked to call 101, or use the Live Chat facility on the police website. The crime reference is 13230487755.
Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111 or online.