Johnson said he will be wearing a brace and taking pills without any activity for a week, at which point he will be re-evaluated.
"Nothing torn or any of that stuff, so that's a pretty good sign," Johnson said. "We'll see how it goes in a week."
Johnson was placed on the 15-day disabled list on Thursday after leaving Wednesday night's game following his first at-bat, when he felt sharp pain and weakness fouling off a changeup.
He struck out swinging on the next pitch and was removed for pinch-hitter Ryan Flaherty in the fourth inning.
"I hope that he can get back where it doesn't cause him any pain anymore, and he gets, more importantly I think, the strength back," manager Buck Showalter said. "There's not any real structural changes."
Johnson's right wrist has been a trouble spot throughout his career. He underwent season-ending surgery on it in May 2010 when he was with the Yankees, and also missed all of the 2000 season and most of '08 due to right wrist issues.
After testing the wrist rigorously in Spring Training, Showalter said the Orioles were careful to limit Johnson's batting practice to keep from aggravating it.
Johnson had been healthy throughout 2012 and was starting to come into his own, hitting .295 in May and June after an 0-for-26 April.
"I'm not going to talk about him like past tense," Showalter said. "You could see why he's been coveted and wanted on clubs, and we hope that we can get him back where he can do that again."