The Scottish SPCA said the animals can often end up in their rescue centres when children lose interest.
The charity issued a reminder that abandonment is an offence and anyone found guilty of doing so could be banned from keeping animals for life.
Janet Kirkpatrick, senior animal care assistant at the charity's centre in Hamilton, South Lanarkshire, said: "It's not just dogs and cats being abandoned, it's what we call our small furries – be it rabbits, guinea pigs, gerbils.
"Mum and dad get a rabbit or guinea pig for Christmas, kids lose interest because it's not doing things like sitting or begging, or because of the cleaning involved. We end up getting them in here, or in a lot of cases the rabbits are abandoned, as in put out in the street or the countryside."
The Scottish SPCA's nine centres have 162 small furries, with some rescued after being found dumped in the street.
l An animal charity has shut its doors to newly rescued animals after thieves broke in three times since Christmas Day, stealing equipment and leaving animals traumatised.
Dogs Trust Glasgow has been forced to close while police carry out an investigation at its headquarters in Uddingston.
Sandra Lawton, the trust's rehoming centre manager, said: "My team and I are heart-broken. Some of our dogs nearest to the areas of the break-ins are now showing signs of distress and were clearly terrified by the intruders. Our priority is ensuring our dogs feel settled and calm again."