Moonachie Police Sgt. Tom Schmidt says the rush of water left about 5 feet of water in the streets within 45 minutes.
The police and fire departments are flooded.
Officials are using boats to try to rescue about 800 people living in a trailer park and other stranded residents.
There are no reports of injuries or deaths.
Local authorities initially reported a levee had broken. But Gov. Chris Christie says a berm overflowed.