The hospital, which is in Sha Tin, said the incident had happened at about 2 pm, while the man was waiting to be admitted for isolation.
The man is described as being about 1.65 metres tall, of medium build, and with short greyish hair.
The hospital said, according to CCTV footage, he was wearing a red, checked, long-sleeve shirt and dark trousers, as he left.
It said security guards had tried to find the man, both on the hospital grounds and nearby, shortly after staff realised he was not there.
The hospital is asking the public to contact the police, or the hospital hotline on 3505 2786, if they know his whereabouts.