Police describe Johnson as being of around 170cm tall and of thin build and heavily tattooed on both arms.
He was last seen wearing a dark top, black pants and was likely to be wearing Nike scuffs.
"He has a medical condition that requires frequent medication so it's important that anyone who knows where he is, or might have seen Matthew, contacts police immediately on 111," the spokeswoman said.
Members of the public who have sighted Johnson can also call police on 105 quoting file number 210212/2524.
