Nelson underwent exploratory surgery on his right shoulder Tuesday afternoon, when it was discovered a repair would be necessary.
He suffered the injury last week while diving back to first base as a runner and was diagnosed with a right rotator cuff strain and partial anterior labrum tear. He has already been ruled out for the season.
"This is probably somewhere in the middle of the scenarios," Stearns said. "The best-case scenario Jimmy told you guys was the doctor goes in there and it's a relatively minor procedure, and he has the potential to be back at the front end of next year. Obviously, we don't think that is going to be the case. We do think he is going to miss a chunk of next year.
"But on the plus side, we do think he's going to be able to pitch in the major leagues for us at some point next year. We don't know exactly when, but we'll see how the rehab goes."
The Brewers believe Nelson's recovery will be helped by the fact his labrum tear was a nonthrowing injury.
"Any surgery to a pitcher's arm, elbow, shoulder, you're obviously concerned," manager Craig Counsell said. "But they feel more common now, and guys do come back from them. We know that Jimmy will put in the nth degree of work to come back, so I'm planning on having him back next year. I'm sure we'll have that conversation frequently about patience."
Nelson, 28, was having perhaps the best season of his career for the Brewers, who lost 6-4 to the Pittsburgh Pirates on Wednesday and sit just one game out for an NL wild-card spot. He went 12-6 and led the team with a 3.49 ERA and 199 strikeouts in 175⅓ innings.
"Look, I don't think you ever completely recover from losing a player like Jimmy Nelson. But this is an opportunity for somebody else," Counsell said. "Who that is, we feel like we certainly have a lot of candidates to get that opportunity. That's really what it means to me: It's going to be an opportunity for someone else. Jimmy is going to push himself to get back as quickly as he can."
The Associated Press contributed to this report.