The vehicle carrying 70 passengers was partially crushed by the tree near St Andrews this afternoon as high winds driven by Storm Ali tore across the country.
The University of Dundee squad were travelling to the Fife town for a match when the incident happened about 12:45pm.
The driver and all but one of the students escaped injury after falling branches badly damaged the top of the coach.
One student required stiches after being hurt.
The medical treatment was done at the scene by a paramedic.
The incident happened at Kincaple Farm Cottages, just east of Guardbridge. Fishers Tours was operating the coach,
Company director Jim Cosgrove said the coach was a write-off, but the driver had stayed on to continue his day’s work.
The students were en rouse to the University of St Andrews Football Club Varsity 2018.
A Dundee University spokesman said: “We can confirm that a coach carrying students representing the university’s football teams was damaged by a tree while travelling to St Andrews.
“One person was treated at the scene by paramedics for a minor head injury before continuing with the rest of the party to their destination to fulfil their fixtures.”