The weather service said the F-1 tornado cut a path two miles in length, 250 yards wide with max winds of 90 m.p.h.
Three to four houses were damaged in Plumsted Township, along with numerous tree trunks snapped.
A few telephone poles were also bent and snapped. Much of the damage reported along Long Swamp Road, Colliers Mills Road and County Route 539.
NWS crews were on the ground in other locations, specifically in Monmouth County, to see if there were any other tornadoes.
Most of the town of Perth Amboy was without power Friday morning.
Perth Amboy Mayor Wilda Diaz declared a state of emergency in her Middlesex County community, ordering city employees to launch a "massive cleanup."
No injuries were reported. But authorities said the storms - which contained strong winds, heavy rains and dangerous lightning - knocked down trees and power lines in many towns and caused some moderate property damage. The weather also forced the cancellations of some sporting events, including several high school football games and a minor league baseball playoff game in Trenton.
About 40,000 customers statewide were without power early Thursday night. A little over 3,800 were still out Friday afternoon.
The storm hit southwestern areas of the state around 5 p.m. and quickly moved north, spawning winds that reached more than 60 mph in some areas.
The storm also affected travel in some areas, as police directed traffic in areas where the storm knocked out traffic lights.
The National Weather Service is also investigating whether a tornado touched down Thursday evening during the storm. Tornado warnings had been issued for Staten Island, Brooklyn and Queens.
(The Associated Press contributed to this report)