The incident occurred at around 1.30pm at Horns Cross.
The police said the three vehicles were: a blue Vauxhall Astra, a blue Frontera and a white Mercedes articulated lorry.
A female occupant of one of the two cars was taken to North Devon Hospital but her injuries are not thought to be serious.
The lorry driver was stuck in his cab after the crash but was not injured.
Two fire engines were called from Bideford.