Austin Peay, the Ohio Valley Conference champion, is 27-3 and seeded 14th. The game will be the first matchup between UNC and APSU.
Also playing in Boulder are host Colorado, the No. 6 seed, and BYU, the No. 11 seed.
The No. 3 seed is UNC's highest since 1998, when the Tar Heels were seeded second. Carolina will make the program's 15th appearance in the NCAA field.
"I'm glad to see the bracket and know who we're going to play," UNC coach Sylvia Hatchell said Sunday evening. "I don't know a lot about Austin Peay yet, but I know the coach, Susie Gardner. She was an outstanding player at Georgia and has done a great job at Austin Peay.
"We're excited to go play in Colorado. Charlotte (Smith-Taylor) played out there in the ABL and Tracey Williams lived in Colorado Springs when she worked at USA Basketball. I've spent a lot of time out there, too, and we've got a lot of friends there."