It happened just after 7:30 a.m. on Mendham Road.
Police say one vehicle was traveling east and the other west when the limb came crashing down on both vehicles.
One person suffered minor injuries. The other was taken to an area hospital and pronounced dead.
The accident happened the morning after a powerful nor'easter tore through the Tri-State area, causing flooding and other problems.
ALSO READ | Nor'easter causes flooded roads, stuck cars in New Jersey
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