Redick, The Associated Press Player of the Year, also was charged with unlawful use of highways for making an illegal U-turn.
The 21-year-old was also charged with unlawful use of highways and his drivers license was temporarily revoked, according to records, CBS News reports.
Redick, who has a Virginia driver's license, lost his driving privileges in North Carolina for 30 days, police spokeswoman Kammie Michael said.
Redick was released on $1,000 bond shortly after being taken before a Durham County magistrate. He is to appear in court July 17. The arresting officer wrote in his report that Redick had "very glassy eyes, strong odor of alcohol coming from breath."
Redick had a blood-alcohol level of 0.11 percent. 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.
On Monday, he canceled a scheduled Wednesday workout with the Orlando Magic, who have the No. 11 pick in the draft. Magic spokesman Joel Glass declined to say why Redick backed out, and no workout has been rescheduled.
"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 the case.
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 last season.
"J.J. is an outstanding student-athlete of the highest character," his agent, Arn Tellem, said in a statement. "He is (an) exemplary role model and a credit to his family and the entire Duke community. This is nothing more than an isolated incident."