Miles said he will continue with his duties as head coach while undergoing a quarantine process.
"Although I will physically not be able to attend practice for the time being, I will be using the technology available for remote working to stay connected during staff meetings, meetings with players, etc.," he said.
Kansas athletic director Jeff Long said the school believes Miles could return for the team's Oct. 17 matchup against West Virginia.
"Based on the other test results, no other coaches tested positive. As long as Coach Miles does not develop symptoms or have a fever, we anticipate he will be able to coach the West Virginia game on Oct. 17," Long said in a statement.
Long's statement is not fully accurate because Miles said he had a cold Wednesday. That would imply he is having some symptoms, which may hamper his ability to return for the game against West Virginia. The Centers for Disease Control and Prevention recommends an isolation period of at least 10 days, which is particularly important for symptomatic carriers.
Kansas is off to an 0-3 start in Miles' second season, bringing his overall mark to 3-12 at the school. The Jayhawks have not had a winning football season since 2008.