The incident happened at the junction with the B937, near Collessie, at about 21:05 on Saturday.
Police have appealed for witnesses to the accident which involved a silver Volkswagen Beetle.
Sgt James Henry, of Police Scotland, said: "Anyone who may have seen a man walking in the area of the A91 around that time on Saturday, or who witnessed the incident, please get in touch."

Investigations by The Daily Telegraph newspaper have revealed several cases of alleged fraud in football.
Coleman says he has never taken or been offered a 'bung' and believes the sport's governing bodies should operate a zero tolerance policy on corruption.
"If anyone is caught then they should be removed from the game permanently and that's it, good night," he said.
He continued: "It's sad, but I have zero respect for anyone caught.
"If you earn £50,000 a year, that's a good salary to the man in the street. If you're earning £50,000 a week then why are you after more? It's just greed.
"Unfortunately we are all tarnished with the same brush. We are all involved in an industry where there is corruption from the very top.
"But what are we going to do about it if someone is caught? Will it just be a rap of the knuckles or will they be banished?
"If there is evidence against someone and they are found guilty then get rid of them from the game and they should never be allowed back."
Barnsley suspended assistant manager Tommy Wright after he was named in a Daily Telegraph investigation in which he was filmed apparently being given an envelope of money in return for allegedly helping Barnsley to sign players from a fake Far East Firm.
Sam Allardyce lasted only 67 days as England manager before leaving in disgrace after the same newspaper said he advised undercover reporters posing as businessmen how to "get around" transfer rules.
Coleman says he has sympathy for Allardyce.
"I'm really disappointed for Sam. I was with him last week at a coaches' conference in Paris and I know he will be absolutely devastated," Coleman added.
"I've known Sam for a long time and I know how much he wanted the job and how proud he was to get it. So I'm gutted for him that he has lost it through events off the pitch rather than on it.
"He has made a mistake and admitted that. It's a shame that someone of his experience let their guard down for five minutes and lost their job over it."
However, Coleman made clear he has no desires to succeed Allardyce, answering unequivocally when asked if he would be interested in the position.
"My answer would a big fat no," he said.
A man has died after being hit by a car on the A91 in Fife.
[NEXT_CONCEPT]
Wales manager Chris Coleman says anyone found guilty of corruption in football should be banned for life.