A white BMW 420 coupe struck the woman under a railway bridge on Bradford Road, Dewsbury at about 10:10 GMT, police said.
The road was closed for four hours, with a section of the nearby Lidl car park also cordoned off.
The arrested 21-year-old man remains in police custody for questioning.
Sgt Carl Quinn, of West Yorkshire Police, said: "Anyone who saw the collision or the manner in which the BMW was being driven prior to it, is asked to contact the major collision and enquiry team."

Victory over her Czech opponent would have put Konta in with a chance of breaking into the top 20 of the world rankings for the first time.
Novak Djokovic reached the last 16 of the men's singes with a 7-5 7-5 win over German Phillipe Kohlschreiber.
Rafael Nadal beat fellow Spaniard Fernando Verdasco 6-0 7-6 (11-9).
Two-time champion Serena Williams defeated Kateryna Bondarenko 6-2 6-2 to earn a quarter-final with Simona Halep.

The Independent Police Complaints Commission said there were six fatal police shootings between April 2016 to March 2017, up from three in 2015/16.
The number of deaths in police road traffic incidents rose by 11 to 32 - the biggest total in eight years.
The six shootings included that of Westminster attacker Khalid Masood.
It is the highest number in 12 years.
Twenty-eight of the road traffic deaths were related to police pursuits of vehicles.
Since the IPCC was set up in 2004, there have never been more than a handful of fatal police shootings in a year, so the fact there have been six is unlikely to raise alarm bells.
And, as the watchdog points out, the number has to be set in context: there were more than 14,700 police firearms operations during the same 12-month period - the vast majority pass off without a shot being fired, let alone anyone dying.
However, the sharp rise in pursuit-related deaths - after a concerted effort by police and the IPCC to reduce the number of such casualties - will prompt searching questions. Of the 28 who died, 18 were either passengers in the suspect vehicle or other road users.
Does the rise simply reflect an upsurge in criminal activity? Is it because suspects have become increasingly reckless? Or have police standards on the roads slipped?
The IPCC and the National Police Chiefs' Council will have to get to the bottom of it quickly.
Dame Anne Owers, chairwoman of the IPCC, said the six fatal shootings occurred across six forces.
The shooting of Khalid Masood was the only one related to terrorism.
The watchdog said the investigation into that case and two others had been completed and all three found no evidence of any misconduct by firearms officers.
In addition, another inquiry, which is still ongoing, is also yet to find any evidence of wrongdoing by police.
Investigations into two other shootings are still to conclude.
The National Police Chiefs Council and the IPCC will examine whether changes to police pursuit safety or training are needed after the rise in road traffic deaths, added Dame Anne.
The IPPC data also showed there were 14 deaths in police custody - the second lowest figure it has recorded.
Eight of the 14 people who died were reported to have mental health problems.

The 28-year-old tested positive for a banned substance just days before heading to the Olympic Games in Rio.
He claimed the result was orchestrated to stop him speaking out about politics in Indian sports, saying: "Their intention is to shut me up."
Navin Agarwal, director general of India's anti-doping agency, denied samples could have been tampered with.
Singh said he denied "all the allegations of doping that I am accused of".
"I am being targeted and it's a clear case of conspiracy against me," he said. "My sample has been tampered with
"I have been speaking out against the politics in sports in India and how badly athletes are treated and their poor training facilities, and this has riled many powerful people in the country."
Singh is the second Rio-bound Indian athlete to fail a doping test after wrestler Narsingh Yadav, 26, last week tested positive for a banned steroid.
Yadav has also denied wrongdoing, claiming his food supplements were spiked.
"I believe that there is foul play involved in this entire episode," he told India's NDTV station.
No sanctions for the pair have been announced, and Singh has been asked if he would like to have a second sample tested.
A man has been arrested on suspicion of causing death by dangerous driving after a woman was run over near a supermarket in West Yorkshire.
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British number one Johanna Konta is out of the BNP Paribas Open in Indian Wells following a 7-6 (7-2) 3-6 6-3 defeat by world number 19 Karolina Pliskova.
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The numbers of fatal police shootings and deaths after police pursuits in England and Wales both rose sharply in the last year, the latest figures show.
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