The crash happened before 7:30 a.m. on Alston Avenue and Juniper Street.
School officials said while en route to school, a bus from Rogers-Herr Middle School was hit by a car.
Police said that car ran a stop sign, causing the school bus driver to swerve and hit a Durham city DATA bus.
School officials said students were on the bus but no injuries were reported.
Officials say there was no one on the DATA bus other than the driver, who was not hurt.
Police have yet to release the man's identity; however, officers said he was arrested on outstanding warrants.
Another bus arrived to help take the students to school.
Editor's note: A previous version of this story stated that a Durham Public Schools bus driver was arrested after the crash. Police are now saying it was the driver for another vehicle.