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."
A man has died after being hit by a car on the A91 in Fife.