Officially, at least, the Yankees will be without Aaron Judge for at least a week after formally placing him on the injured list Wednesday with a sprain of the big toe on his right foot. But Judge — who hurt himself on a leaping catch that carried him through the right field fence at Dodger Stadium on Saturday — has no actual timeline for returning to the active roster.

“No next steps,” Manager Aaron Boone said. “Think about getting a shot in your big toe, into the joint. You’ve got to get over that, then we’ll see where we’re at.”

Judge received a platelet-rich plasma injection in the toe on Tuesday night, when the Yankees lost to the Chicago White Sox, 3-2. If the swelling from the shot subsides in a few days, as expected, the Yankees will have a clearer outline of how Judge should progress.

This is the second I.L. stint this season for Judge, who missed 10 days last month with a strained right hip. He has still managed to lead the American League in home runs, with 19, and has the best slugging percentage (.674) and on-base plus slugging percentage (1.078) in the majors.

“I guess, technically, you have less margin for error when you take the best player in the sport out of your lineup every day,” Boone said. “But, that said, we’re also getting some key guys back in our lineup, a lineup that, frankly, the last two weeks has been doing a really good job of scoring runs, and scoring runs in different ways.”

For right-handed hitters like Judge, the right big toe is the catalyst for rotating the lower half of the body when they swing. Infielder DJ LeMahieu, who broke the sesamoid bone in his right big toe last season and had subsequent ligament damage in his second toe, was severely hampered by the injury. It cost him most of September and all of the postseason — and came with considerable embarrassment.

“It sounds stupid, because it’s your toe,” LeMahieu said on Wednesday. “But it does have a big effect on a lot.”

LeMahieu said he had seen Judge’s toe, which he called “completely black and blue,” but had not spoken with Judge about the particulars of the injury. He said anyone with a foot injury should prepare to be frustrated.

“The feet heal slow,” LeMahieu said. “If you have another injury, I feel like it’s always like, ‘OK, it’s four to six weeks, this is the rehab, then you’re good to go.’ But with the feet, it’s such a complex thing that there’s no one answer.”

Boone said that Judge’s toe problem, at least, seemed more straightforward than LeMahieu’s injury last season. But the Yankees cannot be sure until Judge begins his recovery, which is on hold for now. Judge will miss at least the rest of this homestand — a doubleheader with Chicago on Thursday and three weekend games with the Boston Red Sox — as well as the first game against the Mets at Citi Field next Tuesday.

The team promoted outfielder Billy McKinney, a left-handed hitter who was batting .274 with nine homers for Class AAA Scranton/Wilkes-Barre, to replace Judge on the active roster. McKinney, 28, played the first two games of his major league career with the Yankees in 2018, and has since played for Toronto, Milwaukee, the Mets, the Los Angeles Dodgers and Oakland.

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