"He's going to be out for a while," Brind'Amour said. "I can't give you any update as length of time, but he's not playing any time soon, I don't think."
The 28-year-old forward played 14:44 in a 4-3 overtime win against the Minnesota Wild on Saturday but sat out the final 3:04 of the third period and didn't play in overtime. He was in his second game back after missing four games with a lower-body injury.
The Hurricanes recalled forward Eetu Luostarinen from Charlotte of the American Hockey League on Sunday.
Haula has 11 points in 16 games. He's fourth on the Hurricanes with eight goals, one fewer than Andrei Svechnikov, Dougie Hamilton and Sebastian Aho, all of whom have played four more games.
The Hurricanes play the Chicago Blackhawks at United Center on Tuesday (8:30 p.m. ET; NBCSCH, FS-CR, NHL.TV).