Police said that no one was injured in the incident that took place around noon today in a new part of the Serbian capital.
The statement identified the man only by his initials, MP, born in 1979.
No other details were immediately available, including the motive for the attack.
Witnesses said no major damage was visible on the restaurant.
Anti-American sentiments are strong among some Serbs because of the 1999 US-led NATO bombing of the country that ended Serbia's control over the former province of Kosovo.