The case came to light when one Shabana went to the hospital to get treatment for her son Imran (3) and daughter Shirin (one-and-half-year).
The 24-year-old woman told police that Wahid Khan, 19, with whom she was living for the last fortnight, frequently beat up the boy and stubbed out burning cigarettes on her daughter's body, a fact also confirmed by M Y Hospital Medical Superintendent V S Bhatia.
The boy's hand was also found to be broken.
The two children are being treated at M Y Hospital. Bhatia said the girl is out of danger.
Indore police had yesterday arrested Wahid, who was later sent to judicial custody. Wahid is currently in jail.