The incident took place in the Sealdah-bound Kalyani Simanta local train on Thursday evening.
The victim identified as Anima Sahu (32), a resident of North 24 Parganas district's Kanchrapara, was rushed to Kalyani's JNM Hospital in critical condition, a railway police officer said.
According to fellow commuters, the youth boarded the unguarded ladies compartment at the Kalyani station as the train was gradually moving out. He attacked the victim with a knife, after she protested against him travelling in that compartment and asked him to get down immediately.
"The youth stabbed the woman multiple times with a knife. He jumped off the train from the wrong side when a few hawkers got onto the compartment hearing the screams of the victim. The accused is yet to be nabbed," the RPF officer said.
The incident left the passengers in a state of panic as a lot of women jumped out of the moving train. However, none of them sustained any serious injuries.
"We need to talk to the woman in detail once she recuperates. We are trying to identify the assailant and nab him. It could not immediately be ascertained that the woman was stabbed on the account of asking the youth to deboard the ladies compartment. We are not ruling out any old enmity with the victim," the RPF officer added.
( With inputs from IANS )