German was placed on the restricted list while he undergoes treatment, according to the Yankees.
"It is critical that Domingo completely focuses on addressing his health and well-being," the team said. "We will respect his privacy as he begins this process."
General manager Brian Cashman told reporters that German won't pitch again this season.
"Certainly it's a very serious issue that affects way too many people, unfortunately, and hopefully the steps that are being taken today will really benefit him for the remaining part of his life because it's a very serious problem that you need to address head on and these treatment places are significant steps hopefully to helping him get the tools to solve it," Cashman said.
German, who turns 31 on Friday, authored the 24th perfect game in major league history June 28 at Oakland, but the outing was one of his few bright spots this season. Overall, he's 5-7 with a 4.56 ERA.
On Monday, he initially was scratched from a start against the Tampa Bay Rays because of discomfort in his armpit, but then entered the game in relief, throwing five scoreless innings of two-hit ball in a 5-1 loss.
Since arriving in the majors six years ago, German has had trouble on and off the field. He served a 10-game suspension in May after getting ejected from a game in Toronto for using an illegal sticky substance on the mound. He was also banned 81 games by Major League Baseball earlier in his career over an alleged domestic violence incident.
He's been brilliant at times for the Yankees, the highlight: an 11-0 victory over the Athletics when he pitched the majors' first perfect game since 2012. He called the game a tribute to his uncle, who died two days earlier, leaving German crying in the clubhouse.
German joined Don Larsen (1956), David Wells (1998) and David Cone (1999) as Yankees to pitch perfect games.
German went 18-4 in 2019 with the Yankees but was put on administrative leave late that season while MLB investigated an alleged domestic violence incident involving his girlfriend.
He missed the entire pandemic-shortened 2020 season and playoffs while serving the 81-game suspension, then met face-to-face with Yankees teammates and made a public apology at spring training when he returned to the club in February 2021.
"I'm just worried right now for the person and the immediate family," Cashman said Wednesday. "Domingo Germán has certainly been a part of the Yankee family and he's dealing with a very serious issue and I certainly think we're all going to keep him in our prayers as he takes very important but necessary steps in trying to deal with this problem."
It's the second time in eight years that a Yankees starting pitcher has entered treatment for alcohol abuse during the season. CC Sabathia left the team in October 2015 to check into a rehab center just before New York's playoff loss to Houston in the AL wild-card game.
"It just affects you as a human being," ace Gerrit Cole said after New York's 7-2 win over Tampa Bay on Wednesday night. "You care about your teammates. You care about your teammates' families. So it's a sad situation and you want the best for Domingo."
Information from The Associated Press was used in this report.