Troopers responded to a report of an auto accident on the parkway, near Exit 25, Newbridge Road, at about 7:56 p.m.
Philip Coppola, 46, who was driving a white Chrysler, told troopers he struck the side of an unknown vehicle that left the scene.
As they spoke to Coppola, troopers said they "detected a strong odor of an alcoholic beverage," according to a news release.
Coppola failed sobriety tests, police said, providing a breath-analyzer reading of 0.19 percent, and was arrested.
He is charged with DWI and traffic violations and is scheduled to appear May 11 in First District Count in Hempstead.