POLICE are investigating two stabbings that occurred overnight in Melbourne.

At the first incident, a woman was stabbed in a Port Melbourne apartment in Florence St around 9.45pm.

A man was yelling outside a ground floor flat when the occupant opened her door and told him to leave.

The man then slashed the front security door with a knife.

A neighbour came out of her adjoining flat and told the man to leave when the woman, 30, received a slash wound to the back of her head before the man ran from the scene.

The second incident occurred at an apartment block in Sutton St, North Melbourne just after midnight.

Emergency services were called to the apartment where they found a 55-year-old male with lacerations to the head.

The alleged offender, a 48-year-old North Melbourne woman, was located in a nearby street not long after and arrested without incident.

Anyone with information on either incident is urged to call Crime Stoppers on 1800 333 000.