The accused, who also suffered burn injuries, has been arrested today, they said.
The incident occurred last night when the girl's parents were not at home.
According to the police, the 23-year-old man had asked the girl to come out of the house but she refused. Angered over this, he returned with a bottle of kerosene, poured it on her and set her ablaze.
The girl was rushed to a nearby hospital by her neighbours and later shifted to Kottayam Medical College, where her condition was stated to be serious with over 80 per cent burn injuries, they said.