Morrow has been moved into the starting rotation as a replacement for left-hander Erik Bedard, who was scratched from Saturday night's scheduled start because of what manager Don Wakamatsu described as "slight inflammation" in his throwing shoulder.
Bedard, who has a 5-2 record and a 2.37 ERA, will take a breather until the Mariners' series opener on Friday night against the D-backs at Safeco Field.
"He felt it a little in his last start," said Wakamatsu, referring to Bedard's outing against the Twins on Sunday in Seattle. "This is precautionary. He could probably pitch tomorrow, but it's safer to push him back. To keep him healthy all year, we felt it's best to push him back one start."
It is the second time this season that the left-hander has missed a start. He was skipped once last month after straining his groin.
Morrow, who started the season as the Mariners' closer, but was replaced by David Aardsma after back-to-back blown saves against the Rangers May 13-14, recently asked the organization to switch him back to starting.
The initial plan was to send Morrow to Triple-A Tacoma, possibly this weekend when right-handed reliever Roy Corcoran is expected to be activated from the 15-day disabled list. That move probably will happen prior to Saturday night's game and the corresponding move figures to be backup catcher Guillermo Quiroz being sent back to Double-A West Tennessee.
Morrow last pitched on Wednesday night in Baltimore, tossing a season-high 2 1/3 innings.
"The main thing is try to be conservative with my pitches and try to give them the best game I can until the guys come in after me."
Morrow hopes the 60 or so pitches he scheduled for will take him at least through five innings.
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.