Police: Officers have said they are hunting a single suspect who was carrying a small but sharp knife and may have been wearing a mask.
Police also said he was wearing dark clothing and was riding a mountain bike.
The first stabbing took place at around 8:10pm on Ormeau Avenue, the second knife attack happened at around 8:45pm on Donegall Square West, and the third took place at around 9:30pm on University Road.
Police in Northern Ireland said all three women were taken to hospital with injuries that are not thought to be life-threatening.
They have since been discharged.
A fourth attack was reported to officers after a woman was punched in the neck on Lisburn Road at around 9pm.
A fifth attack was reported after a woman was punched in the head by a man on a bicycle on Dublin Road at around 8:55pm on Monday.
The assault was reported on Tuesday morning and police believe it may be linked to the other four incidents.
All five women are aged between 19 and 22.
Officers do not believe robbery was a motive and some of the victims were accompanied by friends.Chief Superintendent Simon Walls said: “Just be vigilant, know where you are.
“If you are going out, try to be with a friend or in groups.”
Such attacks are extremely rare in Northern Ireland and officers have stepped up patrols.
Mr Walls added: “Police are taking this investigation incredibly.
“We accept the fear that this type of attack causes. We wish to say that incidents like this in Belfast and across Northern Ireland are indeed rare.”