Joseph Cafferkey, 72, from the Acomb area of the city, was last seen by a neighbour on Wednesday, North Yorkshire Police said.
Officers have been carrying out searches to find him since he was reported missing on Friday, but he has not yet been located, the force added.
It said his family are “very concerned” for his welfare, as his disappearance is out of character.
North Yorkshire Police is urging anyone who sees Mr Cafferkey, or knows where he is, to contact them straight away. Call 101, select option 1, and quote reference number 12200173603.