"Coach Kill is taking time to continue treatment and focus on managing his epilepsy," Teague said in an official release.
"Tracy Claeys will serve as the acting head coach until Coach Kill is ready to return. Coach Kill will remain in very close contact with the team and his staff and provide direction and support as needed. Our support for Coach Kill is unwavering and we look forward to his return to full-time coaching duties."
Kill had been planning to return to the team after a seizure early Saturday morning caused him to miss last weekend's 42-13 loss to Michigan. This is his fifth seizure-related absence since 2011, when he took the job at Minnesota.
University president Eric Kaler said Teague and Kill are "managing this health situation, as it relates to our football program, in the most straightforward and caring manner possible."
"My wife Rebecca, myself and our two daughters want to thank everyone for their prayers and concerns during the last few weeks," Kill said. "This was a difficult decision to make, but the right decision.
"Our staff has been together a long time and I have full confidence in Coach Claeys and them during my time away," Kill said. "Every decision that will be made will be in the best interest of the players and the program. I look forward to returning to the Minnesota sideline on a full-time basis soon."