The person apparently fled into a wooded area along the shoulder of the westbound lanes of I-40 near NC 54.
Police tried to persuade the suspect - a man allegedly involved in a domestic dispute overnight - to surrender, but the man told police he had a gun, which prompted a standoff.
The man apparently got caught in a thick briar patch during the standoff, making it impossible for a police dog to get to him.
Police apprehended the unidentified man around 7:30 a.m.
At least four Cary police patrol cars were parked along I-40 for several hours, but no lanes were closed.
Further details about the incident have not been released.