State police said 22 other people on the bus, including students and athletic staff, had only minor injuries.
The driver, whose identity was not immediately released, was taken by helicopter to a Boston hospital.
The bus was southbound on Interstate 95 at about 8:30 p.m. when it crossed the median, went across the northbound lane and down an embankment into woods near Georgetown, a town of about 8,000 residents 30 miles from Boston.
Georgetown Fire Chief Al Beardsley said it was a miracle no other cars were involved.
"This is a very heavily traveled road, day and night, and for a bus that size to basically catapult across the road, I couldn't imagine being northbound and seeing that thing coming at me," Beardsley said at the scene.
The University of Maine said Coach Richard Barron was treated for minor facial cuts and three others—players Ashleigh Roberts and Corinne Wellington, and Samantha Wheeler, the team's director of basketball operations—were taken to a hospital for observation. The team was en route to play Boston University on Wednesday night. That game has been postponed, according to the basketball schedule posted on UMaine's website.
"We're very thankful that this accident was not any worse than it was," Robert Dana, vice president for student affairs and dean of students, said in a statement. "The thoughts of the entire University of Maine community are with the bus driver and the team as they contend with this very frightening event."
Beardsley said authorities are still investigating what caused the driver to veer off the highway, which has four lanes in each direction and a broad median. Police say their preliminary investigation indicates he had a medical issue.
The bus remained upright and appeared to have plowed through a roadside snowbank, knocked down a mile marker, and crashed into woods along the road before coming to rest pointing down an embankment.
"He hit pretty high up on the tree, you can see marks," Beardsley said.
The bus was owned by the John T. Cyr & Sons Inc. bus line of Old Town, Maine. A man who answered the phone at the company's office late Tuesday said company officials were gathering information and had notified their insurance carrier.
UMaine Athletic Director Steve Abbott told WHDH-TV in Boston that it was "quite a traumatic ride" and that although passengers were shaken up none were seriously hurt. He said the university has used the bus company extensively and found it to be a "terrific carrier."
A state police car that stopped at the scene was struck by another car. The trooper who had been driving it was taken to a hospital with what appeared to be minor injuries, police said. Police said the driver of the car was not hurt.
Earlier this month, a bus crash in Boston injured 35 people, including high school students and chaperones, from Pennsylvania. The coach slammed into a 10-foot-high overpass on Feb. 2 while returning to the Philadelphia area from a trip to Harvard University.