Ten other students on the bus were injured, two of them critically.
Indianapolis Metro Police identified the driver as Thomas Spencer II, 60, of Indianapolis. Donasty Smith, 5, Indianapolis, was the student killed in the crash.
The crash happened just before 8:00 a.m.
The bus, which was transporting students to Lighthouse Charter School, was headed southbound when it smashed into one of the support pillars for a train bridge.
It's unclear at this point why the bus driver lost control.
Two children are still listed in critical condition. Eight other children suffered bumps and bruises. The other students on board were not injured.