Police said the demonstrator used petrol, and a Palestinian flag was found at the scene, outside the mission in Atlanta. The person's gender and age remain unclear.
A security guard who attempted to intervene was also injured. According to police, the protester arrived at the facility at 12:17 local time (17:17 GMT).
"We believe this building remains safe and we do not see any threat here," Mr Schierbaum said. "We believe this was an act of political protest."
The guard suffered burns to their wrist and leg during the incident, Atlanta Fire Chief Roderick Smith told reporters. Both the protester and the guard were taken to a local hospital.
In a statement, the consul general of [Zionism] to the southeast US, Anata Sultan-Dadon, said that the diplomatic mission is "saddened to learn of the self-immolation at the entrance to the office building".
"It is tragic to see the hate and incitement toward Israel expressed in such a horrific way," she added.
"The sanctity of life is our highest value. Our prayers are with the security officer who was injured while trying to prevent this tragic act".
I remember Wynn, partly thanks to a somewhat tacky spoken-word poem about the matter