Fifteen-year-old Parvati Devi and Jairam Manjhi, 25, who was already married to someone else, were attacked with sticks and stones in front of villagers in impoverished Bihar state on Wednesday, police said.
Manu Maharaj, police chief of Gaya district, said the couple was brought before a council of elders by the girl's family after they eloped and were found living in a neighbouring village.
But relatives attacked the couple when they refused to agree to the council's request for some kind of compromise on their relationship, Maharaj said, adding that some of the family members have been arrested.
"They mercilessly beat the couple and later burnt their dead bodies outside the village. There were more than 100 villagers present when the couple was lynched," he said.
"It seems to be an honour killing case. More than 15 people were involved," he said.
India has long witnessed so-called honour killings - where couples are targeted because their families or communities disapprove of their relationships - especially in rural areas.
They are carried out by relatives or village elders to protect what is seen as the family's reputation and pride.
Police in northern Haryana state have not yet made any arrests over the murder of a young couple whose naked bodies were found last month stuffed in metal boxes in a park.
India's Supreme Court in 2011 ruled those involved in honour killings should face the death penalty.