Judge, a three-time MVP, is likely to miss out on the wildcard round, which begins next Tuesday. The Yankees will likely take on their arch-rivals Boston Red Sox in the best-of-three series.
"We are planning as if Judge was not part of it," said New York's manager Aaron Boone regarding Judge's participation in the series.
The 34-year-old was on the team's injuryd list last Saturday, three days after leaving a game versus the Minnesota Twins due to a calf strain.
Boone mentioned on Tuesday that the injury is "moderate grade".
Judge received a PPP injection on Monday and will not take part in any physical activities in the next few days, according to his manager.
The slugger suffered the injury just a week after returning from a fractured rib that had him out for three months.
The Yankees, who last won the World Series in 2009, are currently second in the AL East with a 89-66 record, six games back of leaders the Tampa Bay Rays.
Bar an unexpected collapse from the Rays in the last week of the regular season, the Yankees will almost certainly face the Red Sox in the AL wildcard round for the second year running.