Police say the man, about age 20, barged into the girl's room at 2:30 a.m. Monday.
After raping her, the suspect set her on fire, said Kiran Sivakumar, police superintendent of Noida, a suburb of New Delhi.
The girl suffered severe burns, Sivakumar said.
"They were in a relationship for over a year," Abhishek Yadav, the chief investigator in the case, told CNN. An investigation is underway to determine why he allegedly set her on fire, Yadav said.
The horrifying assault took place a day before International Women's Day
On Tuesday, Indian President Pranab Mukherjee underscored the need for greater efforts to ensure the safety of women in the South Asian nation, saying, "It is intolerable that in this day and age, women are still being exposed to barbaric brutality and violence because they are women.
"Violence or fear of violence reduces the freedom and development of everyone particularly, our women and children. But more than that, it diminishes our society when it allows such inhuman treatment of its women rather than guarantee their safety, security and equal rights," Mukherjee told an award ceremony marking International Women's Day.
"On this day, let us all, (the) government, civil society and public at large, pledge to work together for developing relevant legal, administrative and other measures to ensure the safety and security of our mothers and sisters."
In 2012, a savage gang-rape of a physiotherapy student on a bus
in the Indian capital stirred global outrage and brought focus on the country's attitudes and treatment of women.
India has since toughened its rape laws, with stringent punishments not only for sexual assaults but also for voyeurism and stalking.
The number of rape cases reported in India rose to 36,735 in 2014 -- up some threefold since 2012, according to the National Crime Records Bureau. However, the rise doesn't necessarily mean more women were raped, but rather indicates more cases were reported. Twenty-eight percent of the reported cases turned into convictions, the bureau said.