The bus, operated by Megabus and carrying 68 passengers, veered off the road at around 5:30 a.m. on Interstate 65 in Seymour, State Police Trooper Clifton Elston said.
The most serious injury was a broken collarbone, and most of the others were treated for minor cuts, Trooper Tommy Walker said. Two of the 26 passengers brought to Schneck Medical Center in Seymour refused treatment.
The bus driver, Christopher Kelley of Olympia Fields, Illinois, told police he was in the left lane and moving to the right lane when he lost control and slid onto the grassy median, Trooper Matt Holley said.
Walker said speed and the weather may have contributed to the accident.
"Conditions changed from being dry and cloudy and cold to we got some winds and then some snow flurries," he said.
Walker said several other accidents were reported in the area, which is about 60 miles southeast of Indianapolis. The cause of the accident is being investigated.
The bus had stopped in Indianapolis and also planned to make stops in Louisville, Kentucky, and Nashville and Chattanooga, Tennessee, said a Megabus spokesman, Sean Hughes.
He said the company was assisting the authorities with their investigation.
State police said the uninjured were taken to Seymour Middle School, where the Red Cross set up a shelter. By late Saturday afternoon all of the passengers were en route to their destinations, police said.
In October, a Megabus following the same route was involved in a crash on I-65 just south of Indianapolis, in which several people were injured.