"We can control it a little bit more [if he's on the DL]. We feel it's the best move for Brandon and for the club."
Morrow, who is 0-1 with a 4.05 ERA and 5-for-5 in converting save chances this season, was scheduled to throw a bullpen session prior to Saturday night's game against the Athletics at Safeco Field.
"We'll see how he reacts out of it tomorrow," Wakamatsu said. "If everything is good, we will continue with bullpens every other day until he's eligible to come off the DL."
Morrow said last week in Anaheim that the current ailment is his most common. But in previous incidences, the discomfort was gone within a couple of days.
"It has been a little more prolonged this time, and we think it's better to be proactive with it and give him a few more days to get him back to feeling better," Wakamatsu said. "He's actually on the mend already, but this is safer for him. Since he hasn't been able to get into a game, we are going to have him throw a bullpen and go from there."
Wakamatsu said Stark would pitch in the "fifth to seventh" innings and right-hander David Aardsma would continue to close games. He has three saves so far this season, giving Seattle one of the best one-two closing tandems in the Major Leagues.
If Aardsma is not available, rookie Shawn Kelley would get the closing call.
Stark, 34, was 0-0 with a 3.97 ERA in seven relief appearances with Tacoma, holding opposing hitters to a .214 batting average.
The veteran, who has undergone two Tommy John elbow ligament replacement surgeries, was the Mariners' fourth-round selection in the 1996 Draft. He made his MLB debut on Sept. 15, 1999, and has a 15-13 career record with a 5.78 ERA.
His most recent game in the Majors occurred with the Rockies on July 19, 2004, against the Padres.
Stark made the short drive from Tacoma to Safeco Field late Saturday morning and had to pause a few times to keep his emotions in check.
"Just to walk in here today was unbelievable," he said. "This is one of the greatest days of my life."
The Mariners announced later on Saturday that they have signed right-handed pitcher Steven Shell to a Minor League contract. Shell will report to Tacoma.
The 26-year-old began the season on the Nationals' Opening Day roster and made four appearances out of their bullpen, going 0-0 with a 5.40 ERA. He was designated for assignment on April 20.
Shell made his Major League debut with the Nationals last season, going 2-2 with two saves and a 2.16 ERA in 39 appearances. His ERA was tops in the National League and third-best in the Majors among rookies logging at least 50 innings.