Wright is expected to rejoin the team Tuesday in Port St. Lucie. He has yet to play in a game this spring and there is no firm timetable when he might.
"Basically a cortisone shot is intended to eliminate or mitigate inflammation," general manager Sandy Alderson said. "What the doctors told us was that he had essentially plateaued. There was a little bit of soreness. Not a great deal, but this will accelerate the recovery process.
"I don't want to speculate. I really don't have any information."
Added manager Terry Collins, "David was close. I think that this was just an added precaution to speed along the process of him getting better. I know when he comes back he'll have a time frame in mind. Then we've got to see where he is by the weekend."
The way this spring has gone for the Mets, though, it's not surprising that other medical news wasn't as upbeat. Left-handed reliever Tim Byrdak is scheduled to undergo surgery to repair a torn meniscus in his left knee.
Alderson's estimate is that the team's only proven situational lefty could miss about six weeks. Alderson added, however, that he doesn't necessarily feel the need to begin exploring the trade market.
"Josh Edgin has pitched well for us. We're going to bring him over to Major League camp, effective immediately," the GM said. "Garrett Olson has pitched well for us. We have Robert Carson in camp. Daniel Herrera. So we'll look at that. Obviously this will impact our left-handed relief. We'll just have to evaluate things as we go forward. I would suspect that Byrdak will not be available to us for some portion of the regular season. We'll have to accommodate that.
"Ideally, certainly we'd [like to have a left-hander in the bullpen]. And this injury notwithstanding, I would expect that we still would. Actually we're a little better situated with left-handed relief pitching than we were last spring. That doesn't mean we won't miss Tim, but we have a number of options this year that we didn't have last year."
The Mets also recently auditioned C.J. Nitkowski, but haven't decided whether to sign him. "We probably won't get into that for another day or two," Alderson said.
Edgin has the makings of becoming one of those Spring Training fairy tale stories. Even though he's 25 years old and spent all last year pitching at Class A with Savannah and Port St. Lucie, the Mets decided Sunday to move him to big league camp.
He came in to pitch in the eighth inning of what ended up as a 7-7 tie in 10 innings. With two outs and runners on first and third, he gave up an RBI double to Andy Dirks before getting out of the inning.
In the ninth, Collins had right-handed hitting Avisail Garcia walked intentionally in part so he could see him face left-handers Quinton Berry and Eric Patterson; Edgin struck them both out.
Is it too much to ask for Edgin to make the jump all the way from Class A?
"I'm not sure," Collins said. "Because I've seen unexpected guys like that, especially situational guys, surprise you. He's not intimidated. He's not scared when he goes out there. He's got a great arm. In the role he'd be used in, I certainly think he might be able to handle it.
"We've been looking at [the other left-handers] in a little different light than when Byrdak was here. Right now I think we have to focus a little more on what they can bring to the table, how durable they might be. How effective against left-handed hitters they've been and how they might be able to be more effective."
Said Edgin, who has faced 12 batters this spring and allowed one hit: "It's terrible [that Byrdak got hurt]. I hope he gets back fine. But that's the way it works, I guess."
After going 2-1 with a 3.82 in 72 appearances last season, the 38-year-old Byrdak signed a $1 million contract extension. He also flew to New York on Sunday.
Said starter Jonathan Niese: "It's going to affect us. He's a good guy to get lefties out. But there are other guys who are going to step up and do the job."
Paul Hagen is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.