The blaze broke out on the eighth floor in the DeWitt-Clinton Houses on Lexington Avenue just before 1:15 a.m.
Four people were hurt, with the man sustaining the most serious injuries. He was rushed to the burn unit at NewYork-Presbyterian/Weill Cornell Medical Center.
A 28-year-old man, a 20-year-old woman and a 1-year-old girl who all live in the same apartment were also injured. They were treated at Mount Sinai Hospital.
Authorities believe the incident began as a dispute between the man and a female friend, possibly over a missing cell phone.
The fire apparently started in a pile of clothes in his apartment, and gasoline may have been used as an accelerant.
The woman was taken into custody and being questioned by detectives.