McKenzie was stopped after he cut through a gas station lot at about 9:30 p.m., said Little Falls police Lt. Salvatore Calafiore. A Breathalyzer test found McKenzie's blood-alcohol level was above New Jersey's legal limit of 0.08. He was taken to police headquarters and released later that night, Calafiore said.
In a statement issued by the Giants on Friday afternoon after McKenzie had left the stadium, the lineman expressed remorse about the incident.
"I am prepared to deal with the consequences of that situation from both a legal standpoint and as a player in the National Football League," McKenzie said.
Giants coach Tom Coughlin said the team was aware of the arrest and had spoken with McKenzie. He did not address if it would affect McKenzie's status for Sunday's game against the Baltimore Ravens.
"The legal process will take its course, and the league will handle this matter," Coughlin said. "Nobody will be harder on Kareem than Kareem himself. He is very conscientious and has been a first-class citizen since he arrived here with our organization."
A New Jersey native, he was drafted out of Penn State in the third round by the New York Jets in 2001 and signed with the Giants as a free agent in 2005.