Judge, who is yet to feature in any MLB spring training games, will rest for at least a fortnight before being re-evaluated.
It is another blow for the Yankees ahead of their March 26 opener against the Baltimore Orioles, with slugger Giancarlo Stanton (calf) already sidelined.
"At least we have an answer, so now we can start working on a solution," Judge said on Friday. "But overall, I'm just mad.
"I want to be out there with my team, especially in Spring Training. We have a good team here, a good club. We have a lot of goals here in 2020, and I want to be out there. But the first thing is you've got to get this healed, get it right and then we can move forward."
There is the possibility of surgery for two-time All-Star and 2017 Silver Slugger Judge, who said: "The fact that the bone is healing, progressing that way, there's really no need to go down that route.
"If it wasn't healing, wasn't going the way we wanted it to go, then, yeah, that's a possibility.''
Yankees manager Aaron Boone added: "It was to a point where he needed to start getting some answers.
"Now we have some answers and a plan of attack in place. Hopefully, it is a situation where it is healing and it won't be something that ends up being too long."