Sean Caldwell was last seen at Crosshouse Hospital on Kilmarnock Road, Kilmarnock, at around 2.45pm on Friday, June 14.
The 30-year-old of known to visit the Paisley and Ayrshire areas and police are appealing for the public’s help to trace him.
There are concerns that Sean needs medical treatment and officers have been checking relevant CCTV in the area.
Sergeant Claire Walker said: “There are concerns that Sean may require medical attention and we are concerned for his safety and wellbeing.
“I am appealing to anyone who may have seen Sean or who has any information as to his whereabouts to get in touch with us.
“It’s important we confirm he is safe and well.”
Sean is around 6ft 5ins tall with a medium build, blue eyes, brown hair and facial hair.
He was last seen wearing a salmon pink football top with a dark coloured hooded top and navy blue shorts.
A CCTV image appears to show a bandage wrapped around his head.
Anyone with information is asked to contact police via 101, quoting incident number 2084 of Friday, June 14.