The police said they have arrested the girl's parents, and her "husband" for illegally marrying her despite having a wife and a son from his first marriage.
According to the police, the couple was living in a rented house in Balakati on the outskirts of Bhubaneswar after eloping from Betagadia village in Balasore district, about 150km east of Bhubaneswar. They got married two months ago in a temple.
The police said Uma's parents, 45-year-old Radha Gobinda Mallick and 40-year-old Santilata, came to her rented house on Thursday and tried to persuade her to end the marriage and return home.
When Uma refused to do so, her parents asked Nigamananda to fetch an auto-rickshaw on Friday so that they could go back to Balasore.
When he left home, they tied up the woman, gagged her and set her afire after pouring kerosene on her. She died on the spot, police said.