Smoak felt his oblique tighten up during Saturday's game against the Rangers and hasn't played since.
The 25-year-old said he's fine fielding his position and the main thing holding him back now is being able to swing full-out left-handed.
"Right-handed feels fine," said the switch-hitter. "Left-handed, it's a lot better today than yesterday."
Smoak said he had a similar injury, but much worse, in his first year of pro ball when he missed more than a month at Double-A.
"I've had it before on the left side," he said. "Thank God I was smarter than I normally am. I'm normally going to play through it, but when I felt what I felt, I knew what I had done before and didn't want to feel that again. I tried to get out of there and take care of it."
Smoak said he might be available to pinch-hit on Wednesday, at least right-handed, and certainly feels he'll be ready to help out in the next few days.
"I can pinch-run, too," Smoak said with a grin.
Kendrys Morales got the start at first base again on Wednesday.
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.