Joan Crilly was struck by a Skoda Octavia car on Campbell Street at about 16:05 on 22 December.
She was taken to Inverclyde Royal Hospital then later transferred to the Queen Elizabeth University Hospital.
She died on Wednesday as a result of her injuries. The 73-year-old car driver was uninjured.
Officers have appealed for witnesses to come forward.
Mrs Crilly was married and had two children, police said.
A 69-year-old woman has died after being seriously injured when she was hit by private hire vehicle as she crossed a road in Greenock.