Wheelchair user William Strathearn, 43, was last seen at his home in the Capital’s Abbey Street around 1pm on Friday, March 19.
He is described as white and of very thin build, with brown shoulder-length hair and a goatee-type beard.
His disappearance is “out of character”, according to police.
Officers are now appealing to members of the public for information to find Mr Strathearn.
Sergeant Carol Moir, of Gayfield Police Station, said: “Officers are looking to trace William to ensure that he is safe and well.
“He is without regular medication that he requires and the lack of contact is out of character for him.
“I would urge anyone who has seen William, or who has any information regarding his whereabouts, to contact Gayfield Police Station through 101 quoting reference number 1263 of March 19.”