Morris Wilson was reported missing at 6pm after being seen in the Chapeltown area of the city.
The 43-year-old is from Leeds but it is believed he may be in the Wakefield area.
Detective Inspector David Roberts, of Leeds District CID, said: “We are concerned for Morris’s welfare and urgently need to find him and check that he is okay.
“We would like to hear from anyone who has seen him or who has any information that could assist is locating him.”
Morris is described as white, 5ft 10in and of heavy build, with short, receding hair. He was last seen unshaven and wearing grey tracksuit bottoms, a grey t-shirt, a blue jacket and Adidas trainers.
Anyone with information is asked to contact Leeds District CID via 101, quoting log number 1498 of August 15.