The 21-year-old man was on Flinders Street between Elizabeth and Queen Streets at around 5.30am when he was approached by a teenage girl, police said.
The teenager, who was in a group of around 10-15 other people, then allegedly stabbed him.
He suffered non-life threatening injuries and was taken to hospital.
The victim and the teenage girl were not known to each other.
No arrests have been made.
In a separate incident nearby, a woman was arrested after allegedly assaulting two other women.
The woman was believed to have been brandishing a broken glass bottle when the incident took place at around 7.30am at the corner of Elizabeth Street and Flinders Lane.
One woman received minor injuries and was taken to hospital for treatment.
The alleged offender then assaulted a second female on Flinders Street and Elizabeth Street.
The second woman was assessed by paramedics at the scene.
A 35-year-old woman, from north Melbourne, was arrested and remains in custody.
An investigation into the alleged assaults remains ongoing.
Anyone with information about either incident is urged to contact police or Crime Stoppers on 1800 333 000.
