Hackney was injured in the third quarter of Saturday's 27-24 loss to Texas Christian. He was hit by TCU linebacker Josh Goolsby just as he released a pass.
UAB (3-4) was leading 24-19 when he departed.
"Darrell is our guy and has been our guy," said Coach Watson Brown. "He's been our main leader and it was an ugly blow. We knew he was hurt. The team has to adjust to that."
Hackney, a sophomore, threw for 1,659 yards this season with nine touchdowns and six interceptions.
With Hackney sidelined, freshman Chris Williams will move into the starting lineup and start Saturday against No. 5 Georgia.
Williams, a freshman from New Orleans, sat out the 2002 season, and began this fall as No. 3 at left cornerback. In three games, he is 4-of-13 for 50 yards and one interception.