Animal rescuers were called by the “distressed” woman who said she had a “strange wild animal” leaping about.
Volunteer Gemma Warner said: “We asked her to describe it so we knew and she just said it was small with a bushy tail.
“We thought it was just a squirrel or maybe a baby fox.”
Instead they found a marmoset sat on the kitchen worktop.
The primate, the size of a large cat, is native to South and Central America.
Gemma, from animal charity Wings and Paws, said: “He was very skinny and hungry but he was clever enough to know he needed to find the humans.
“We assume he must have been a pet which was sadly dumped or released when the owner no longer wanted him.”
He was removed from the relieved woman’s property in Wolverhampton and yesterday was at an animal rescue centre.
The organisation is trying to find a home for the white-headed marmoset — who they named Marcel.
He is tame and friendly with humans, sitting on their lap and shoulder and grooming them.
Gemma added: “It’s lucky we found him because the cold would have killed him if he’d been left on the streets of Wolverhampton.
“It’s not their usual habitat as you can imagine.”
Forest-dwelling marmosets mostly eat sap and gum from trees, but they also munch insects, frogs and baby birds.
It is legal in the UK to keep them as pets but the RSPCA advises against it, as they need a warm climate and lots of stimulation.
It said: “Unfortunately, it’s technically legal to own a marmoset in the UK, but we’re campaigning against primates as pets and calling for the governments of England and Wales to change this.”