Salazar (11-4) was placed on the 15-day disabled list with right elbow inflammation Tuesday, a day after the shortest outing of his career. An MRI showed no structural damage, and Salazar won't throw for five to seven days.
"We're pretty confident that just about when his DL time is up, he'll be ready to resume starting again," Indians manager Terry Francona said.
Salazar lasted two innings and allowed six runs, including three homers, against Minnesota in a 12-5 defeat Monday.
The loss was his first since May 22. He told reporters his elbow had bothered him for several weeks. The right-hander has an 8.84 ERA over his past four starts, totaling only 18⅓ innings.
Salazar underwent Tommy John surgery in 2010, and Francona said the MRI was done in part to help the pitcher's peace of mind.
"We all know that Danny is learning that you maybe not always are 100 percent, and trying to find a way to get through that during a game," Francona said. "But we also need to be cognizant that, 'OK, if this is what can help Danny be really good, we need to help him.'"
Mike Clevinger will be recalled from Triple-A Columbus to start Thursday against the Twins.
Outfielder Brandon Guyer, acquired from Tampa Bay on Monday, was added to the 25-man roster.