Kollam Rural SP and the district child protection officer have been asked to file a report within 15 days on the incident.
According to the police, the child's mother, who had estranged relations with her husband, was staying in her friend's house at Kundra.
When she was not at home, her friend's husband assaulted the child and allegedly burnt her with a hot stove yesterday.
Hearing the child's cries, neighbours rushed and took her to hospital, the police said.
The man has been arrested, police said.
Last week, a seven-year-old girl in Kollam district was allegedly sexually assaulted and killed by her uncle.