Baxter was sent down to Las Vegas, along with first baseman Ike Davis on June 9 when Satin was called up. Davis has also since returned to the Mets.
Baxter batted .212 with no home runs and four RBIs in 85 at-bats over 41 games with the Mets earlier this season.
"Anytime you get sent down you're always hoping you get a chance to come back. You don't take that for granted," Baxter said. "I really wish it wasn't on these terms. Watching David getting hurt last night, nobody really wants to see that. He is the heart of this team.
"Somebody is going to have to step up and we're going to have to try to pick up the slack for him. It's a big hole to fill. I don't know if one guy can do it. It's probably going to have to come from a couple of us. Hopefully we do."
The Mets were already dealing with multiple injuries in the bullpen on Friday before Wright got hurt.
New York closer Bobby Parnell is unavailable until at least Sunday because of a stiff neck. Left-handed setup man Josh Edgin went on the disabled list on Friday, and is expected to be sidelined 4 to 6 weeks because of a stress fracture in a rib.
Veteran reliever Pedro Feliciano was brought up on Friday from Las Vegas and he made his first major league appearance since 2010.
Carlos Torres, who was scheduled to be Saturday's starter, was returned to the bullpen on Friday, and he earned the win with a two-inning effort. He will stay as a reliever for now as the Mets are abandoning their six-man rotation until Jonathon Niese returns soon from a shoulder injury.
Jeremy Hefner was moved up from his Sunday start to pitch in Torres' place against the Royals on Saturday. Zack Wheeler, used as a pinch-runner on Friday, will take the mound Sunday.