Officer Lee Lepe, a spokesperson for the Metropolitan Police Department, on Monday confirmed the airman's death.
The Pentagon said the death was a "tragic event" and US Defence Secretary Lloyd Austin was following the situation.
Pentagon spokesman Major General Patrick Ryder told reporters that he was not aware of any other acts of protest by service members against the war.
The airman had been hospitalised in critical condition on Sunday after US Secret Service officers put out the flames, DC Fire and EMS had said earlier.
The man, wearing military fatigues, broadcast the incident live over the internet.
"I will no longer be complicit in genocide," the man said before dousing himself in a clear liquid and setting himself on fire, screaming "Free Palestine," according to a video seen by Reuters.
The latest incident comes amid ongoing pro-Palestinian and pro-Israeli protests in the United States following the Hamas attack on Israel that killed 1200 Israelis and seized 253 hostages in a cross-border incident on October 7 last year.
Israeli forces then waged a military campaign against the Palestinian Islamist group that rules Gaza, destroying much of the coastal enclave, with nearly 30,000 people confirmed killed, according to Palestinian health officials.
Israel's embassies have drawn continued protest against the war. In December, a woman protesting the war set herself on fire outside the Israeli Consulate in Atlanta.
