The attack happened at a property in the Dunluce Avenue area in the early hours of this morning, Thursday, July 2.
All three have been arrested on suspicion of attempted murder and are currently assisting police with enquiries.
The men are currently being held at Musgrave PSNI station in Belfast city centre.
The 33 year old victim was taken to hospital for treatment to his injuries and his condition is being described as serious but stable.
Detective Inspector Mary White said: “I am appealing to anyone who was in the area around 6.30 am this morning noticed any suspicious activity or witnessed the incident to contact detectives at Musgrave on the non emergency number 101.
“Or alternatively they can contact crimestoppers on 0800 555 111.”
The Ambulance Service said one of its crews responded to a report of a possible stabbing at Dunluce Avenue around 6.40 am this morning.
Paramedics treated one man at the scene who was in a serious condition and took him to the accident and emergency department at the Royal Victoria Hospital.