At least four of the injured were reported in serious condition.
The crash near Orebro caused backups as emergency crews cleared the highway, the Swedish news agency TT reported.
"This means that we are working with redirecting all conceivable resources in the hospital so we can take in all the patients," hospital spokeswoman Ulrika Julin told TT.
The school bus was carrying children on a trip to Stockholm from Skara, officials said.
"Many people started screaming and I wondered what happened," said 16-year-old Emelie Johannesson, who told the Aftonbladet newspaper she was sleeping at the time of the crash.