The Blue Jays are optimistic the injury isn't serious, but a timetable for his return won't be known until the medical staff takes a closer look. For now, Rasmus is considered day to day.
"He jammed his wrist into the fence," Blue Jays manager John Gibbons said. "The trainers are checking with him. He didn't think it was too bad yesterday, but we've been wrong on those before."
Jose Bautista got the start at designated hitter for the third consecutive game on Thursday. He has yet to play the outfield since he sustained a minor left hamstring injury, but that is expected to change in the relatively near future.
The hope is that Bautista will be ready to play the field at some point during the four-game series in Oakland and could be cleared as soon as Friday. In the meantime, Toronto has used a temporary solution of putting Edwin Encarnacion in left field so the club can get both Bautista and Adam Lind into the lineup.
"He's not quite ready, we want to make sure he's good and ready," Gibbons said of Bautista. "Hopefully in the next couple of days."
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.