Mets starting pitcher Tylor Megill walks through the dugout after...

Mets starting pitcher Tylor Megill walks through the dugout after coming out of the game during the fourth inning against the Milwaukee Brewers in an MLB baseball game at Citi Field on Thursday, June 16, 2022. Credit: Kathleen Malone-Van Dyke

Tylor Megill is out indefinitely after being diagnosed with a right shoulder strain and landing on the injured list Friday.

The Mets said in a statement that their immediate plan for the righthander is “for him to be shut down from throwing and re-evaluated in four weeks.” Even a best-case scenario would have Megill sidelined at least into August.

“I’m hoping on the 29th day he’s throwing,” manager Buck Showalter said. “I don’t know yet, but I think that would be good news. When you’re talking about the shoulder, when I heard the four weeks, I was actually kind of upbeat about it.”

Showalter also vaguely mentioned that the Mets will “take some steps and see what other things we can possibly do to speed up the process,” but he did not get into specifics.

That leaves the Mets with short-term rotation questions but, they hope, long-term answers in the form of Max Scherzer and Jacob deGrom.

The first problems they need to figure out: Who will start on Monday against the Marlins (David Peterson’s spot; he is expected to go on the paternity list any day now) and Tuesday against the Astros (Megill’s spot)?

Righthander Trevor Williams, who has made five starts in 12 appearances this year, is a prime candidate for one of those games. Showalter also mentioned as possibilities righthander Adonis Medina, whom the Mets like as a potential starter but who has not been able to build up his pitch count in part because he has bounced between the majors and Triple-A Syracuse so often, and righthander Stephen Nogosek, a reliever who has pitched as many as three innings at a time. Medina rejoined the Mets on Friday.

The Mets will need to drop one of their 14 pitchers by Monday, when MLB will begin enforcing the 13-pitcher limit.

“It’s not like you can [have] 14 or 15 and cover those innings,” Showalter said. “I’m not quite sure what that’s all about. If you’re going to 13, you might as well go to 12 and really see who can handle their pitching. But they didn’t ask me.”

Showalter added: “It’s going to be a challenge. For a lot of teams. I’m hoping in the future it’s an advantage for us. If we’re getting deep in games with starters, it could be an advantage for us.”

The good news for the rotation: The Mets have three days off in an eight-day stretch beginning Thursday, temporarily limiting the need for a No. 5 starter.

Also, Scherzer is penciled in to make a rehab start Tuesday and is expected back soon — potentially June 26 in Miami or shortly thereafter, if all continues to go well with his strained left oblique.

The situation with deGrom, who has missed the whole season with a stress reaction in his right shoulder blade, is less clear. He said he completed another bullpen session Friday but declined to say whether he simulated multiple innings, which was expected to be the case. Showalter said he didn’t know what deGrom did.

Now the Mets are down three of their top six starters: both aces and the guy who ended up starting Opening Day.

Megill’s season has been split in two: a 2.43 ERA in six starts during the first month but a 15.75 ERA in three starts since. He missed three-plus weeks with right biceps tendinitis. Showalter said the Mets don’t believe the injuries are connected.

“Sometimes it comes back to it’s just not a normal thing to do to your body,” he said. “Put your arm over your head and jerk it down violently every fifth day for 100 times.”