The Eastern Railway PRO confirming the attack said that the incident occured on the Sealdah south section on Sunday night.
The victim was travelling to Kalyanpur from Jadavpur by down Sealdah-Diamond Harbour local, the official said.
The youth, who had his face covered with a black cloth, managed to escape from the train after hurling acid at the woman shortly after she had boarded the train to go to Kalyanpur, the PRO said.
When the train reached Kalyanpur, fellow passengers took the injured women to Baruipur Sub-divisional Hospital from where they were shifted to MR Bangur Hospital, the PRO said.
The Baruipur GRP arrested a promoter, Swarup Halder, in connection with the incident yesterday after the victim's father lodged a complaint, GRP DSP Md Ansar Zua said.
According to the complaint, the promoter, Swarup Halder, had earlier threatened the family over a property related issue.