Morales was removed from Saturday's game against the Yankees due to lower back stiffness, but was back in the lineup at designated hitter Sunday and then played first base Monday.
The 29-year-old is leading the Mariners with a .292 batting average and 35 RBIs, and is tied for third on the club with eight home runs in 63 games.
Smoak has been on the 15-day disabled list since May 30 with a strained oblique. He took batting practice for the first time Tuesday, and manager Eric Wedge said Smoak is close to being sent out on a Minor League rehab assignment with Triple-Tacoma.
"He's going to take BP again tomorrow," Wedge said. "If that goes well, we'd like to get him out hopefully as soon as Thursday."
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.