Barker, the UK starter going into the season, left last week's game against New Mexico State after the first series with a back injury.
The staff later revealed that he's had periodic back issues since the summer and that there is growing concern about it being a "chronic" situation. The third-year sophomore from Burlington, Ky., has not practiced this week and on Wednesday met with a specialist.
"He has an injury that does not require surgery at this point in time," Stoops said, "(but) he will be out for a significant amount of time. I have no idea how long that will be. When I say significant, he's out for the foreseeable future, the next two, three, four weeks. After that, we'll re-evaluate him and see where he's at.
"He's disappointed, as you can imagine... I really feel for him because he's put a lot of time and energy and work to get to this position, and it's tough on him."
Barker has played in all three games for Kentucky (1-2, 0-1 SEC), which plays host to South Carolina (2-1, 1-1 SEC) on Saturday at Commonwealth Stadium. He had thrown for 334 yards and four touchdowns -- most of which came in the first half of the season opener against Southern Miss -- but was also intercepted five times and lost two fumbles. He was benched in favor of Stephen Johnson in a 45-7 loss at Florida, but returned to start last week against New Mexico State.
After Barker was intercepted on the third play of the game, he did not return. Johnson, a junior college transfer, finished the game with 310 yards passing, 51 yards rushing and three touchdown passes in the Cats' 62-42 win.
"We knew he was a good player, but I didn't know he'd have that type of game with those numbers," Stoops said. "You take away that first series, and he was absolutely remarkable."
Kentucky is preparing freshman Gunnar Hoak as the backup quarterback this week. The Cats had hoped to redshirt the talented prospect from Ohio, but depth at the position may force him into action earlier than anticipated.
"If Stephen goes down, Gunnar will go in," Stoops said. "And Luke (Wright) will be ready as well."
Wright is a walk-on transfer from the University of Cincinnati who got a few snaps late in UK's blowout win last week.