The incident occurred at 2.05pm when the car, a red Jaguar driven by a 70-year-old Swiss man, collided into the wall of a house, Lucerne cantonal police said.
The car bounced off the wall and struck the woman who was walking on the pavement toward St. Paul’s church, police said.
The woman, who has not immediately identified, suffered serious injuries and died on the spot, police said.
The driver had stopped at a red light but when the light turned green he accelerated “massively” and his vehicle struck the wall, police said, citing witnesses who saw the accident.
The driver was uninjured.
The cause of the accident was not clear and an investigation is under way to find out what happened.
Property damage totalled 50,000 francs.
The Paulusplatz, a square near the St. Paul’s church, was closed for two hours and traffic was diverted because of the accident, police said.
Public transport was unaffected.