Dettori has not ridden in Britain since October 2023 when he won the Champion Stakes on King of Steel at Ascot.
But he was due to return to the saddle in the Leger Legends race at Doncaster during the St Leger Festival in September.
H Talent Management referred to Wednesday’s crash as an “accident”.
The collision is believed to have happened just over the border in Cambridgeshire and the county’s police force confirmed it was called to a collision on the A1304 London Road near Six Mile Bottom at about 19:00 BST.
A spokesperson for the force added there were no arrests and an investigation was ongoing into traffic-related offences.
The East of England Ambulance Service said two patients were taken to Addenbrooke’s Hospital for “further assessment and treatment”.
In June 2000, Dettori survived a light aircraft crash in Newmarket which killed the pilot Patrick Mackey.
Fellow jockey Ray Cochrane, who went on to be Dettori’s agent, also survived the plane crash.
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