Police received reports that a man on a bicycle had allegedly been run over by a car near the retail park on Mount Pleasant and the vehicle had then driven off.
The 43-year-old cyclist is still receiving treatment in hospital for chest injuries suffered in the incident around 4.30pm on Wednesday.
His injuries are serious but not thought to be life threatening.
Following initial inquiries police were informed that a suspect had boarded a train to Paris where he was detained by French colleagues.
A spokesman said: "The man will be brought back in due course to be questioned by Humberside Police detectives.
"We are appealing for anyone who saw what happened or who may have dashcam or CCTV footage of the incident to come forward."