Veteran Endy Chavez was called up from Triple-A Tacoma to take Saunders' place, but Wedge said no roster move will be made with Morse since he's not expected to be out that long.
"We've got Chavez up here now. We'll make it work," said Wedge. "It is what it is."
Morse said he hoped to be back by Sunday, though acknowledged he'll likely need to play with some pain once the swelling goes down so he can grip the bat.
"I'm fine," Morse said. "I've had a lot worse things than this. It was just one of those freakish things. It's my pinkie, so I'm not too worried about it."
Morse remained in the game after the pitch by Rangers reliever Tanner Scheppers, which was ruled a swinging strike, then was hit in the shoulder on another 95 mph fastball on the next offering.
"It's a crazy game," Morse said with a shrug.
Morse said he didn't realize the finger was hurt until he got to first base.
"It went numb right away, so [trainer Rick Griffin] was out there telling me to squeeze his hand and I was squeezing pretty good," he said. "The rest of my fingers worked pretty good. Then I got hit the next pitch. When I got to first and tried to take my glove off, it wouldn't come off. When I finally did, it just looked all mangled up."
Jason Bay was sent in to pinch-run for Morse and remained in the game in right field. With Morse and Saunders out, the remaining Mariners outfielders are Franklin Gutierrez, Raul Ibanez, Bay and Chavez.
"We have to keep our heads up and keep battling," Ibanez said. "Nobody is going to feel sorry for you in this game. And we're not going to feel sorry for ourselves. We'll keep fighting."
Morse was 2-for-3 before departing and is hitting .293 with six home runs and nine RBIs in the Mariners' first 11 games.
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.