He “is in very serious condition,” a spokeswoman for Madrid's La Paz hospital told AFP.
Emergency services in Madrid tweeted that the man, in his thirties, had suffered a brain injury.
The accident took place in Madrid during a protest by taxi drivers who blocked off a highway on Tuesday afternoon.
Footage of the incident circulating on social media appears to show the man in question jumping onto the moving vehicle along with at least one other protester.
The impact caused him to roll over uncontrollably on the car bonnet before falling onto the ground and hitting the back of his head. The vehicle then sped off as protesters pursued the driver.
Many online commentators are questioning if the driver could actually be considered to have run over the protester, as the latter willingly leapt into the path of a moving vehicle.
The drivers in the city started an indefinite strike on Monday in protest at competition from ride-hailing services such as Uber or Cabify, also known as VTCs (Tourism Vehicles with Chauffeur).
The Civil Guard police force told AFP the driver of the vehicle involved in Tuesday's accident had turned himself in and was questioned before being released.
However the Civil Guard refused to say whether the car was a VTC, as claimed by the taxi drivers.
There were also clashes in Barcelona, where taxi drivers have been on strike since Friday.
Unauto VTC, the association representing the sector, said 80 VTCs had been damaged in Barcelona and 50 in Madrid during the strike.
On Monday, taxi drivers in Barcelona tried to force their way into the Catalan regional parliament but were held back by police.
Spanish taxi drivers complain that rival drivers from ride-hailing apps compete unfairly since they do not face the same regulations and costs.
They also argue that ride-hailing services are not a taxi service by law and should therefore be booked 12 to 24 hours ahead of time.
Catalonia's regional government met with representatives of the taxi drivers on Tuesday and unveiled a new proposal obliging VTC clients to book their services at least 15 minutes in advance.
However a spokesman for the taxi drivers told Spanish public television that VTC vehicles should have to be booked at least an hour ahead in a big city like Barcelona.
A VTC representative quickly threatened to withdraw from Barcelona after the Catalan government's proposal.
“Unfortunately, the Generalitat (Catalan executive) has decided to yield to the taxi sector's blackmail and we are forced to convey that the VTC services will have to leave the city of Barcelona,” Cabify representative Marta Plana told the media.