The victims were attacked outside 350 West 45th Street around 1:30 a.m. Thursday.
Police say a 19-year-old woman was slashed on left forearm, a 20-year-old man was stabbed in the lower back and a 20-year-old man was slashed on the left shoulder.
The injured people were taken to Bellevue Medical Center with non-life threatening injuries.
Four men -- two 19-year-olds, an 18-year-old and a 26-year-old -- were taken into custody at the scene.
Charges against them are pending. They were all identified as Manhattan residents.
A box cutter, believed to be one of the weapons used, was recovered at the scene.
It appears the victims and suspects got into a dispute in front of a restaurant and then spilled onto Ninth Avenue.
Police closed West 45th Street between Eighth and Ninth avenues for hours as they investigated.