Police said the shooting happened around 5:30 a.m. inside a room at the DoubleTree Suites on Meridian Parkway.
A woman was shot in the upper body. Her condition has not been released.
According to Durham police, the suspect ran into the woods near the hotel parking lot in his underwear.
Officers ran after him and disarmed him. Authorities believe he was under the influence of drugs.
Two officers suffered minor injuries during the struggle.