The collision involved a 36 double decker bus and a blue Vauxhall Zafira and a black Mini Cooper.
It happened at around 12.30pm on the A61 just north of Harrogate town centre, between the Little Wonder roundabout and Killinghall.
A 57-year-old woman who was driving the Mini was taken to hospital, along with ab 28-year-old woman who was driving the Zafira and her two children as well as two passengers from the bus.
Police have said the injuries are not thought to be serious. The bus was substantially damaged in the smash.
The A61 was closed between the Little Wonder roundabout and Killinghall following the collision and was reopened just after 4pm.