It is the second major injury to the position after Terrell Lewis, a projected starter, tore his ACL in July.
"It's unfortunate we've got two of those at the same position -- both guys who would have made a contribution on our team," Saban told reporters in Tuscaloosa.
Allen suffered the injury prior to Saturday, but the exact time frame isn't known. He played in seven games as a freshman last season, totaling six tackles, two quarterback hurries and a forced fumble.
"Passed that, we have Ben Davis and two freshmen," Saban said. "That's basically what we have."
Alabama fans might feel some level of déjà vu, considering the rash of injuries at linebacker last season, when Lewis, Jennings, Miller and Mack Wilson all missed significant time.
Saban said that at this point, the defense can't afford many more injuries.
Saban also confirmed that Matt Womack, who started every game at right tackle last season, will be out four-to-six weeks with a fractured foot sustained earlier in the week.
Alabama opens the season on Sept. 1 against Louisville.