Olga Proctor, 85, was reported missing from Wharfedale General Hospital, in Newall Carr Road, at 12:30pm today.
She was last seen wearing a pink nightie, black trousers and a light blue coat.
She has bruising to her face and a black eye from a recent fall.
Detective Inspector James Entwistle, of Leeds District CID, said: “We are very concerned for Olga’s welfare as she has dementia and may be confused.
“We have officers out searching the area for her and would like to hear from anyone who has seen her or who has any information that could assist us in tracing her.”
Anyone who can help is asked to call 101.