Yelich, 29, will be out a minimum of 10 days, while teammate Jace Peterson has been placed on the COVID-19 injured list, as well, because of contact tracing. He is expected to be out for a week.
"He's in good spirits. He's resting," Stearns said of Yelich on a Tuesday conference call. "It's certainly our hope he can knock this out quickly."
The positive test triggered contact-tracing protocols that delayed Milwaukee's flight to Pittsburgh, where the Brewers open a series against the Pirates on Tuesday night. The team flew there on Tuesday morning instead of Monday night.
"A lot of it feels out of our control. This virus is so communicable that you are fearful it can affect a lot of people," Brewers manager Craig Counsell said. "I don't think we're completely out of the woods, but I think it's a good sign that we haven't had any other concerns with the virus spreading."
Stearns said he believes only Yelich and Peterson will be impacted by the positive testing.
"I'm very confident we've satisfied those protocols and doing everything possible to keep our group healthy and safe," he said. "I do think our group has taken this seriously from the beginning."
Yelich is fully vaccinated, with Stearns noting that the "change" is in the virus, as the mutated Delta variant has become the prominent strain in the country. The former MVP had a mild fever on Monday.
"He has taken the precautions seriously and the guidelines seriously," Stearns said.
Stearns said he felt there would be no disruption in Tuesday's game. Yelich has been out of the lineup several times this season because of an ailing back and now will miss more games because of COVID-19.
"I don't think this has been his favorite year, in totality," Stearns said. "He's dealt with a lot. This is just another challenge that he's going to overcome."
In corresponding roster moves, outfielder Lorenzo Cain will be activated from the injured list and infielder Pablo Reyes is being recalled from Triple-A.