Robert Taylor, 54, from Barnsley, left the hospital at around 5am.
He is described as being 5ft 11ins with short grey hair and stubble. He is thought to be wearing navy tracksuit bottoms, a navy knitted hoody and grey trainers.
Police say he has links to Wortley and they are currently in the area carrying out enquiries.
Anyone with information is asked to contact 101 and quote incident number 132 of September 12.