Catriona Scott, 44, who was a customer service adviser at the Civic Centre for more than 11 years, was waiting at the bus shelter in Briants Avenue at 1.25pm when a Toyota Rav 4 left the road. She was taken to Royal Berkshire Hospital with multiple injuries but died just after 5pm on Tuesday.
Reading Borough Council chief executive, Michael Coughlin, expressing his "great sadness", said: "She was very well liked among her colleagues and she was also known by the many members of the public who she had dealings with on a daily basis.
"I am sure you would like to join me in sending our sincere condolences to Catriona's family and close friends, including the many staff here who knew her well and worked closely with her."
A 12-year-old boy, thought to be her son, remains in a "stable but serious" condition at the John Radcliffe Hospital in Oxford.
Police are still investigating the crash and want anyone with information to call 08458 505 505 or Crimestoppers anonymously on 0800 555 111.