Police said the attacker, a man, walked into the laundromat on 170th Street near College Avenue in Claremont, the Bronx, around 2 a.m. Thursday.
The man then stabbed a 47-year-old man in the back and slashed another man in the leg.
The man slashed in the leg died at the scene, police said, and the 47-year-old victim is in stable condition at a hospital.
The weapon, which appears to be a kitchen cleaver, was recovered at the scene. No arrests were made. The attacker was described as around 5 foot 8 inches and 140 pounds. He was last seen wearing a green and black sweater, black pants and black and white sneakers.
Police have no motive for the stabbings and said it appeared to be random.