Duke University spokesman David Jarmul said Wednesday that parents of students have been notified to pick up their children.
Officials said all of the cases were mild and consistent with normal seasonal flu. They said no students had been hospitalized because of the illness.
The TIP camp is a three-week session for academically gifted teenagers ages 13 to 16. Jarmul said the decision to close the three-week camp early was a precaution. The camp is scheduled to continue until Aug. 1.
A similar program being held at a nearby Duke campus will remain open.
This is the first time in Duke TIP's 29-year history that it has had to cancel the camp before it ended. Duke TIP said it will provide prorated refunds to the families.