Carp, 25, sprained his right shoulder in Seattle's Opening Day game in Tokyo on March 28 and has been on the 15-day disabled list, though he's eligible to return as soon as he's fully healthy.
Tacoma manager Darren Brown told reporters Carp will get his first outfield start on Thursday for the Rainiers. Wedge indicated it would be at least a few more days before he's brought back to Seattle.
"He's moving along," Wedge said. "We just need to get him in the outfield and have him start making that progress. He's swinging the bat well and feels pretty good. But we still need to get him in the outfield for a few [games]. We'll get through this week and see where we are."
Carp, who went 0-for-4 in Tacoma's 2-1 loss at Sacramento on Wednesday, is hitting .167 (4-for-24) with two RBIs through his first six games.
Center fielder Franklin Gutierrez is also on the 15-day DL, having been out since Feb. 28 with a partial tear of his right pectoral muscle. Gutierrez remains in Peoria, Ariz., working with Mariners Minor League players in extended Spring Training intrasquad games.
"Gut is still stretching it out, arm-wise," Wedge said. "He's hitting good and doing a good job down there, but we need to get him stretched out further before we can get him out on a rehab."