Jones-Drew, 28, limped off the field in the second quarter after he was awkwardly twisted to the ground by a Raiders defender. Originally ruled as probable to return, he was downgraded to questionable, but never took another snap in the game.
The three-time Pro Bowl selection has suffered season-ending leg injuries in two of the last three seasons and has a contract set to expire following the 2013 season. Regardless, Bradley wouldn't rule out Jones-Drew for the team's Week 3 game against the Seattle Seahawks.
"We feel like we have a chance to have him on Sunday," Bradley told reporters.
Jones-Drew finished Sunday's game with 27 yards on 10 rushing attempts. He accumulated 45 yards on 15 attempts in a Week 1 game against the Kansas City Chiefs.