Police and paramedics were called to the incident on Cleveland Street in Surry Hills about 4am on Sunday.
Two of the men, aged 18 and 19, were taken to Royal Prince Alfred and St Vincent hospitals with critical injuries.
The third man, a 20-year-old, was in a stable condition at Prince of Wales Hospital.
The 18-year-old, who had stab wounds to his abdomen, was unconscious and bleeding heavily when paramedics arrived on scene, NSW Ambulance Inspector Dominic Wong said.
"There was great concern for all three patients.
"Paramedics did all they could to stabilise the patients before transporting them to various hospitals for further emergency care."
The 19-year-old is being treated for critical stab wounds to his chest, while the 20-year-old sustained injuries to his arms.Â
"Any injuries involving a knife have the potential to be life threatening, especially to the chest and stomach where there is serious risk of damaging a patients vital organs," Mr Wong said.
Police have established a crime scene and will begin investigating, with no arrests so far in relation to the incident.