Kittens should stay with their mothers until they are 6 weeks old. However, you can feed them warm kitten milk through a syringe or eye dropper until they are weaned and can eat kitten food.
The reason the kitten could be skinny is because it might have worms. You could take the kitten to a vet and they will normally prescribe some treatment to get rid of the worms effectively.
Another reason is because this kitten could be the 'runt' of the litter? When cats have large litters, the strongest kittens will always find their milk supply, leaving the little weaker kittens at the back of the queue and hungry. You could try feeding her with a syringe, however NEVER feed cats or kittens cow's milk because it contains lactose and cats are lactose intolerant.
If the kitten is the mum's first litter, she might be a bit dazzled by the whole idea of motherhood and might not be encouraging her kittens to feed from her, even though they should do it by instinct.
I think your best bet is to take the kitten to the vet, get her dewormed when she's old enough and feed her regularly using the eye dropper and warm kitten milk method. She should soon gain some weight.
Good luck with your kitty!