The victim's estranged husband has been arrested for the attack, police said Monday.
"The woman and the baby were sleeping inside their house when acid was thrown on them through a window. While the woman has suffered severe burn injuries on her face and stomach, the baby too was hurt. We have arrested the husband," said a police officer.
The woman, admitted in Rampurhat sub-divisional hospital, said her husband and in-laws repeatedly tortured her forcing her to live at her parents' house.
Despite a ban on the sale of acids, the state has witnessed several incidents of vitriolage in the recent past.
According to the Acid Survivors Foundation Indian (ASFI), a non-government organisation, 83 acid attacks were reported in the state between 2006 and 2013 in which at least 121 people, mostly women, were injured.