Police have arrested a Lilydale man following an alleged stabbing in Melbourne's CBD which left one man fighting for his life and a woman taken to hospital with serious injuries.

A 33-year-old man and a 37-year-old woman were allegedly stabbed at the intersection of Flinders and Elizabeth streets on 15 January after a fight with another man.

A 31-year-old Lilydale man handed himself into police on Friday.

He is in police custody.

Police were called to a brawl outside the 7-Eleven near the intersection of Flinders and Elizabeth streets about 4.25am on Monday morning.