The Kalamazoo County Sheriff's office described the injuries as minor, but said some of the passengers were taken to hospital for treatment.
The crash happened about 10:30 a.m., about 20 kilometres east of Kalamazoo.
Kalamazoo County Sheriff Richard Fuller tells MLive.com that the injured included the bus driver and 10 passengers.
Passengers said most of those who were injured were sitting toward the front of the bus.
"I woke up just saw glass shattering everywhere all over me," Marissa Desimone of the Toronto-area told a local Michigan TV station, Wood TV 8.
Desemone, who was headed with friends to the Lollapalooza concert that starts Friday in Chicago, was sitting directly behind the bus driver. She told the TV station that her head slammed into the glass in front of her and the woman next to her was thrown from her seat.
A Kalamazoo Metro Transit bus was brought to the crash site to get other passengers from the Greyhound bus.
They were taken to a transportation centre in downtown Kalamazoo where they boarded another bus that took them to Chicago.
Greyhound Canada was not immediately available to comment.