Marga Bates, 89, was last seen at her home in Brooklands Court, Seacroft, at about 11pm yesterday (Thursday).
Police are trying to trace Ms Bates, and say they are now "very concerned" for her welfare.
She is described as white, with shoulder-length, blonde hair.
She was possibly wearing blue trousers or jogging bottoms, a vest top and a blue jacket and may also be wearing pyjamas.
Police have warned that she may appear "confused".
Anyone who has seen her or has information about her is asked to contact police on 101, quoting log 0260 of May 18.