Officers said a 24-year-old man was assaulted with a knife on Estcourt Avenue at about 11pm last night and belongings including his wallet and mobile phone were taken.
Both of the victims suffered serious injuries "consistent with knife wounds" and were taken to hospital via ambulance, police said.
A 19-year-old male was arrested in connection with both offences and remains in police custody.
Police are now appealing to the public for them to come forward with any information, if they were approached by anyone on their night out or if they saw anything suspicious in the area.
The suspect is described a white male, slim build and was wearing light blue jogging bottoms, a black puffa jacket which had a hood with a fur trim and black trainers with white trims and has an Eastern European accent.
Detective Inspector James Entwistle, of Leeds CID, said: “These were both violent attacks on members of the public who were enjoying an evening out.
“I would urge anyone who was out last night and has information about either of these incidents, saw anyone behaving suspiciously or recognise anyone in the area matching the above description to come forward and speak to the police as soon as possible.”
Anyone with any information is asked to contact Leeds CID via 101 quoting crime reference number 13180152345 or contact Crimestoppers on 0800 555 111.