Arnav Gupta of Bethesda, Maryland, set himself on fire on Wednesday afternoon at the Ellipse Park, not far from the Washington Monument, in full view of passersby, CNBC reported.
He was taken to a hospital in a critical condition and he later died of his injuries, the police said.
Gupta was reported missing on Wednesday morning and authorities had put out a notice asking for the public's help in finding him.
The Montgomery County Police Department in a Facebook post described Gupta as an Indian male who was last seen by his family when he left his home on Cindy Lane, about 10 miles northwest of the White House, around 9.20 a.m. on Wednesday.
The police said his family was "concerned for Gupta's physical and emotional welfare".
The US Secret Service said that officers responded in "seconds" after Gupta set himself on fire, then began administering first aid and transported him to a local area hospital.
Alina Berzins, 17, an eyewitness to the event, told CNBC that she saw the man "running, and then we saw him covered in flames" while she was visiting the National Mall with two of her cousins.
The Indian man's motive for the act, which has historically been performed as an extreme form of political protest, remains unclear.
( With inputs from IANS )