An off-duty rookie cop died in Brooklyn yesterday after plowing his car into a tree on Kings Highway just minutes after he left work, police said.

Officer Patrick Prince, 22, was going home at around 4 a.m. after a late shift at Brownsville’s 73rd Precinct when he lost control of his car near Beverly Road, pinning him in against the tree.

“It looks like he skidded,” Police Commissioner Ray Kelly said.