Chubb, a senior, has 73 tackles, including 26 for loss, and 10 sacks this season. He has forced three fumbles.
"This is what happens if you just keep working," Wolfpack coach Dave Doeren said in a release. "This wasn't a guy who was a five-star (recruit). This is a guy who made himself into one."
Chubb is rated as the fifth-best prospect for the NFL Draft, according to NFLDraftScout.com.
The other finalists for the award were Alabama safety Minkah Fitzpatrick, Iowa linebacker Josey Jewell, Houston tackle Ed Oliver and Georgia linebacker Roquan Smith. The Nagurski Award has been presented by the Football Writers Association of America since 1993.
The 6-foot-4, 275-pounds Chubb broke his school record for single-season tackles for loss, which he set last year with 22. He had five tackles for loss and two forced fumbles in a win at Boston College last month.
Chubb is also a finalist for another defensive player of the year award, the Bednarik. That award, and several others, will be announced Thursday during the Home Depot College Football Awards Show on ESPN.
N.C. State will play Arizona State in the Sun Bowl in El Paso, Texas, on Dec. 29.