The deer eventually jumped into the water near Third Street, witnesses said.
The deer then swam across the Hudson River to Governors Island.
The animal ran along the rocks on shore for some time before police caught up to it.
Officers from the elite Emergency Services Unit fired a tranquilizer dart at the large deer at about 1:30 p.m.
Police say the sedated deer will be taken to a wildlife park on Staten Island.
ON THE NET: