The shirts were created by the Indianapolis Colts in support of their coach, Chuck Pagano, who was diagnosed with leukemia last week.
Michigan football spokesman Justin Dickens said the shirts will be worn by Hoke and the staff during the day leading up to the game but not during the game itself. He was unsure whether the staff would wear them in warmups.
Hoke and his staff have ties to Pagano. Michigan defensive coordinator Greg Mattison was the defensive coordinator with the Baltimore Ravens when Pagano coached the secondary.
When Mattison left for Michigan, Pagano took over as defensive coordinator and eventually became the coach at Indianapolis.
"I know his brother, John, better being out in San Diego. And Chuck, we met years ago, a long time ago," Hoke said Wednesday. "Coach Mattison and Coach [Curt] Mallory, there's a strong relationship. Family ties with the Mallorys, obviously, and Greg coaching with him."
Hoke added that Pagano is "one of ours. He's our kind of guy, and so we wanted to pay a little tribute to him and also to the cause."
Dickens said Hoke paid for the shirts, valued at $20 each on the Colts website, himself.