Wright had an MRI on his ailing back Monday at the Hospital for Special Surgery.
"I was shocked by it," manager Terry Collins said about the diagnosis. "... He is without a question the face of this team. His presence in this lineup is something we need. We're going to ask other guys to pick it up as of today. But I was shocked and unhappy."
Alderson said the team will get a second opinion from another back specialist at the team's hospital before committing to the disabled list. If the diagnosis holds, Alderson said Wright will rest for 10 days, then can resume baseball activities. Surgery will not be required, according to the GM.
"It would be a nonsurgical course of treatment," Alderson said. "According to the information we have now, it would be rest for the next 10 days or so, with a return to baseball activity [afterward]. We're not talking about something long term, but we are talking about something that may require him to rest for a period of time.
"David himself was surprised by it."
The Mets believe the injury originally occurred April 19 while Wright tried to make a diving tag on Houston's Carlos Lee at third base at Citi Field.
Wright said if the risk of worsening the injury did not exist, he might attempt to play through it. Still, he indicated stiffness the first week has turned to localized pain.
"I knew I did it on the Carlos Lee play at third base," Wright said. "We were playing Houston at home. I don't know what the date was. About the first week, I felt stiff and sore, but I felt that would go away the next couple of weeks. I was on some medication and some anti-inflammatories that really wasn't doing much. That explains it now, because it's not a muscular thing.
"It's what could be a stress fracture. ... It's probably me somewhat being stubborn and not getting it checked out earlier. I don't think it really limited me too much or prohibited me from doing anything. It was just a little uncomfortable."
Wright has been on the DL only once in his career, after getting beaned by San Francisco's Matt Cain in 2009.
"I don't think anyone is concerned with feeling sorry for ourselves," Wright said.
He's hitting just .226 with six homers and 18 RBIs, but he certainly wasn't about to blame the injury on his recent struggles.
"By no means is this thing a cop-out or an excuse for what I've done so far," Wright said. "I've played through it and when I take the field, I expect to play at a certain level, and thus far I haven't been able to play at that level.
"This two weeks, I'm going to get better. I'm going to get back in the lineup and I'm going to start playing at the level I expect."
As for Monday's game against the Marlins, Willie Harris played third base. He went 0-for-4 with two strikeouts as the Mets lost 2-1 in 11 innings.
Alderson said that if Wright is placed on the disabled list, first baseman Nick Evans will be promoted from Triple-A Buffalo to take his roster spot.
Adam Rubin covers the Mets for ESPNNewYork.com. Information from ESPNNewYork.com's Mike Mazzeo and The Associated Press was used in this report.