The tiny creature, thought to be less than a month old, is now being looked after by the Scottish Society for the Prevention of Cruelty to Animals at its national wildlife rescue centre at Fishcross in Clackmannanshire.
Given the name of Susie by staff there, she is being given milk to drink and will soon be weaned onto solid food.
Centre manager Colin Seddon said: “Susie is only 16 grams at the moment and is being given milk every two hours.
“She has been showing an interest in chewing recently, so we’re hoping to try her with solid food soon as weasels start to wean before their eyes are open.
“We have successfully reared other members of the mustelid family before, including badgers, otters, pine martens, stoats and weasels.
“Don’t let how cute Susie is fool you – weasels are Britain’s smallest carnivore. Once fully grown, they are fierce hunters and, due to their size, they are able to pursue mice and voles in their burrows.
“We expect that Susie will weigh approximately 60 grams as an adult, whereas males can weigh up to 170 grams.”
Anyone who discovers an injured or distressed wild animal can call the SSPCA on 03000 999999.
A spokesman for the charity said: “Every year, the Scottish SPCA rescues thousands of sick, injured and orphaned wildlife.
“In 2016, we cared for over 9,300 wild animals – a new record.
“We help every kind of wild animal in Scotland and are the only national animal welfare charity which rescues birds.”