They say at least eighteen others were hurt in the accident at the Fox Hill Supercross event in the town of Diyatalawa.
The Sri Lankan army said among the dead were four race officials as well as spectators, including an eight-year-old girl.
The race is organised by the Sri Lankan military, which has an academy in Diyatalawa, and was its 28th run.
More than one hundred thousand spectators were present.
Eyewitness videos show people rushing towards the scene in the aftermath, while the event was suspended.
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