Investigators weren't immediately sure how many people were on the bus, which can hold 59 passengers, Virginia State Police spokeswoman Corinne Geller said. The injured were taken to Richmond and Fredericksburg-area hospitals.
Geller said the bus ran off I-95 before dawn and turned onto its roof about a quarter mile south of the Carmel Church exit, about 30 miles north of Richmond.
The bus's destination hasn't been released. The cause of the accident hasn't been determined.
Virginia Commonwealth University Medical Center has nine people in stable condition, but no details were released about the extent of their injuries. VCU spokeswoman Anne Buckley says the hospital expects more patients to be transferred there from other hospitals.
Mary Washington Hospital in Fredericksburg treated eight patients, whose injuries ranged from critical to minor. Spokeswoman Deborah Morris says one has been released. Spotsylvania Regional Medical Center officials said in a release that it treated eight people for minor injuries.
The accident shut down the northbound lanes of I-95, which weren't expected to reopen for several hours.
There has been more attention on bus safety following a March 12 accident in New York City in which a speeding bus returning from a Connecticut casino toppled off an elevated highway and hit a utility pole, peeling off the roof. Fifteen passengers were killed and 18 injured.
Federal authorities say nearly 2,800 spot safety checks of passenger buses across the country from March 28 through April 6 resulted in about 10 percent of the vehicles or drivers being taken off the road.
