The crash happened at about 6am yesterday on the A658 between Huby and Pool-in-Wharfedale when the grey Citroën C5 estate taxi, which was heading towards Pool-in-Wharefedale, was involved in the collision with a white Ford Transit tipper van travelling in the opposite direction.
The father, 43, and his daughter, who are from Richmond in North Yorkshire and were rear passengers in the taxi, were taken by ambulance to Leeds General Infirmary.
They suffered chest and abdominal injuries in the crash, although neither of them are not thought to be in a critical condition.
The taxi driver, a man aged 55 and also from Richmond, was taken to Harrogate District Hospital with minor injuries.
The Transit van’s driver, from the Humber area, had to be freed by firefighters. The 50-year-old suffered a suspected broken collar bone and was taken by ambulance to Harrogate District Hospital.
Traffic diversions were put in place to allow North Yorkshire Police to investigate the crash scene and for the vehicles to be recovered. The road re-opened just after 11am yesterday.
Officers have appealed for any witnesses to come forward, especially the drivers of vehicles which were travelling in front of the taxi just before the collision.