Police say the boys were riding on East 4th Street and Avenue S in the Gravesend section when they were struck just after 10 p.m.
It appears the boys were on the same bike, with one of them riding on pegs.
The vehicle that struck the boys fled the scene.
One of the boys was rushed to Lutheran Hospital with a cerebral hemorrhage. He is listed in critical condition.
The other child suffered leg injuries.
Anyone with information is asked to call police.