Dorothy Nightingale was struck in Underhill Lane, in The Scotlands area of the city, on December 4.
The collision happened at about 5.30pm. She was taken to hospital but died later that evening.
The driver of the car stopped at the scene and is assisting police with their inquiries.
The family of Ms Nightingale, who was in her early 80s, have paid tribute to her including her work caring for children in the community.
Her family said: ''Our mum, Dorothy Nightingale, was the kindest, most gentle and loving mum, sister, aunty and nan you could wish for.
"Not only to us, her family, but countless foster kids and troubled youngsters she took on over the years.
"She will be loved and missed forever by all her family and friends.''
Anyone with information about what happened can contact police via Live Chat at west-midlands.police.uk between 8am to midnight, call 101 anytime giving log number 1917 of December 4.