Mohammed Akimi (26) was reported missing to police by staff from Leverndale Hospital.
He was last seen about 8pm on Thursday 11 July 2019.
He is around 5ft. 8 inches in height, with a slim build, a beard and short dark hair, possibly shaved. Mr Akimi speaks broken English, his main languages are Farsi and possibly Dari.
When last seen, he was wearing a black hooded top, grey trousers (which he had rolled up to look like shorts) and black boots.
Inspector Stephen Gow said: “Mr Akimi is a vulnerable man who has some health issues requiring regular medication which he currently does not have access to. He has no known family or friends in Scotland and he does not know the area of Glasgow very well.
“Officers are conducting enquiries, including working with our partners, but as time passes on, our concern for his wellbeing is growing.
“We just want to know Mr Akimi is safe and well. If anyone has seen him or has any information or knowledge as to his whereabouts, please do contact us. If Mr Akimi himself hears our message, I want to reassure him that he has nothing to worry about from the police. We are concerned for his safety and wellbeing and just want to make sure he receives any appropriate medical assistance and support.
“I would urge anyone who has any information which could assist us in locating Mr Akimi to contact us as a matter of urgency.”
Anyone with information is asked to call officers at Govan Police Station via 101, quoting incident number 4432 of Thursday 11 July 2019.