The 30-year-old is being treated in hospital after he was struck by a silver Vauxhall Astra on Colewell Close in Southampton, on Monday.
The man, along with another cyclist, was followed through the Shirley Towers estate by the car at about 22:00 BST.
The car is believed to have been driven on to a grassed area where it struck the cyclist then drove off.
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Hampshire Constabulary said: "We believe this was a deliberate act and as such are investigating the incident as a serious assault."
Anyone who may have seen a car described as "old-style and having a loud exhaust" in the area is urged to contact the force.
A man suffered serious head injuries when he was "deliberately" knocked down in an apparent hit-and-run.