The altercation happened early today as an uptown No. 6 train arrived at Grand Central Terminal.
Police say the fight started when an intoxicated man named Ivan DeLeon bumped into a child while exiting the train.
They say the 38-year-old DeLeon stabbed one man in the chest, one in the arm and one in the stomach.
The child was not harmed. The three men are being treated at Bellevue Hospital.
The man who was stabbed in the chest is in critical but stable condition. The other two suffered less serious injuries.