Delta-Mouse, who is six weeks old, was born with a full body of fur, but it soon started to fall out.
When owner Debbie Ikin from Greater Manchester took him to the vet, they discovered he was suffering from the condition - previously only observed in German Shepherd dogs.
'I thought he was the runt of the litter with a skin condition. I have grown up around rabbits and we have had several litters but I've never seen anything like Delta-Mouse' said Ms Ikin, 40.
When out in the sunshine, little Delta-Mouse has to wear factor 50 suncream to protect his skin, even though his fur has since grown back. He also has to have his eyes bathed each morning as they get stuck together overnight.
Ms Ikin's 10-year-old son Jacob admitted he was scared to hold him at times because the tiny rabbit seemed so fragile. But Delta-Mouse has made an astonishing recovery, and is now 'thriving and very spritely' according to Debbie.
'He's become quite a little celebrity' adds Debbie, 'everyone wants to come round and see him.'
And despite hoping to sell off the rest of the litter, the Ikin family are adamant Delta-Mouse doesn't go anywhere.
'I think after all we've been through with him, we couldn't see him go off to another home.'