Redick, The Associated Press Player of the Year, also was charged with making an illegal U-turn. His driver's license was revoked for 30 days, police spokeswoman Kammie Michael said.
The 21-year-old Redick was released on $1,000 bond shortly after being taken before a Durham County magistrate. He is to appear in court July 17.
Redick had a blood-alcohol level of 0.11. The legal limit for drivers in North Carolina is 0.08.
"I regret what happened last night and want to apologize to my family and the Duke community for the incident," Redick said in a statement issued by the university.
Redick finished his career as the leading scorer in Atlantic Coast Conference history. He is expected to be a high first-round pick in the June 28 NBA draft.
"J.J. knows he made a mistake and regrets it," Duke coach Mike Krzyzewski said in a statement. "He represented the very best in college athletics and exhibited outstanding character at Duke the last four years. He is and will continue to be a credit to the Duke basketball family. As his friend and his coach, he has my total support."
The Duke campus has been roiled the past few months after members of the men's lacrosse team were accused of raping a dancer at a party March 13. Three players have been charged in a case that has polarized the community.
Redick was arrested soon after 1 a.m. when he turned around as he approached a license check point near the Duke campus, Michael said. He pulled into a parking lot of an apartment complex after police pursued him.
"There wasn't a chase. He didn't run from them," Michael said. "He was pretty cooperative."
Redick holds the NCAA career record for 3-pointers. The guard averaged nearly 27 points a game.Visit FOXSports.com for complete sports coverage.