The game will be played Feb. 20, though the time is still undetermined.
The postponement came about 3½ hours before the scheduled tipoff at 9:10 p.m.
UNC athletic director Bubba Cunningham said in a statement that Duke's bus couldn't make it to the Durham campus to pick up the Blue Devils for the 11-mile drive to Chapel Hill. He called the postponement "the best decision to make at this time" due to safety concerns.
Tar Heels coach Roy Williams took the opportunity -- in shorts, no less -- to greet fans who braved the elements to wait in line before the game was postponed.
Atlantic Coast Conference policy states that games will go on during bad weather if teams, officials and operations staffers can make it to the venue.
Information from The Associated Press was used in this report.