White, fourth on the team with eight receptions for 105 yards and two touchdowns, had played the "X" receiver position for the Crimson Tide this season after serving as a backup a year ago.
The 6-foot, 185-pound redshirt sophomore from Houston averaged 11.6 yards per catch in his career.
Cooper, a true freshman and a former four-star prospect from South Florida, caught eight passes and two touchdowns against Ole Miss, sending him into the team lead with 17 catches for 222 yards and three touchdowns.
Backup tailback Dee Hart will also miss the remainder of the season after injuring his knee fielding a punt return.
"The MRI indicated that both Dee and DeAndrew sustained knee injuries that will require surgery and they will be out for the year," coach Nick Saban said in a statement.
It's the second season-ending knee injury to Hart in as many years. He had played in all five games this season, rushing for 88 yards on 21 carries. He also contributed on special teams.
Alabama lost its No. 2 running back for the year only a few weeks ago when Jalston Fowler injured his knee. That leaves Alabama with three scholarship running backs: starter Eddie Lacy and a pair of true freshmen in T.J. Yeldon and Kenyan Drake.
Yeldon entered the year as the co-No. 2 back on the depth chart with Fowler and became the first Alabama freshman to rush for 100 yards in his debut, doing so against Michigan in the season opener. He is second on the team with 292 yards and two touchdowns on 50 carries.
Drake has come on mostly in cleanup duty this season, but he's taken advantage of the opportunities, rushing for 126 yards and three touchdowns on 13 carries.