Several of those on board were injured, Police Scotland said.
One male fan is thought to have had to be cut out of ther wrckage and airlifted to hospital, a relative of one of the injured told The Scotsman.
Other injuries included a woman who suffered cuts to her leg, and another woman who sustained cuts to her head and ear.
The coach overturned at the Crossroads roundabout in Kilmarnock at around 1:15pm.
It is not known if anyone has been seriously injured.
A Police Scotland spokesman: “Police were made aware of crash involving a coach at 1:15pm on the A76 at Crosshouse roundabout.
“Emergency services are on the scene.
“The road is currently closed.”
The coach is thought to have been carrying fans from a Rangers supporters’ club in Ayrshire to Ibrox in Glasgow, where Rangers are playing fellow city club Partick Thistle.