The woman, 35, has been admitted to Kanpur Medical College Hospital and her condition is stated to be serious, they said.
The incident happened last night after two friends - Ram Autar of Pipari village and Dinesh of a nearby village - drank together, police said.
After drinking, Ram Autar left for somewhere. Dinesh then came Ram's home where his wife was taking rest with two children, police said.
He then poured kerosene oil and set her on fire, the spokesperson said.
Her neighbours took the woman to a nearby hospital which referred her to Kanpur Medical College Hospital.
Police have registered a case against Dinesh on the basis of complaints of Ram Autar and are looking for him. The accused is absconding, the spokesperson said.