Wider concerns have been raised over urban fox populations after the London attack left Denny Dolan seriously injured in his bedroom. The infant was treated for hand and facial injuries in Downham but is said to be recovering well.
Evelina Children's Hospital said he had been moved from its high dependency unit into a ward. Denny's finger has also been reattached.
Both Glasgow and Edinburgh city councils said householders should not feed foxes in gardens.
Glasgow City Council's website says: "It is very important that no attempt is made to try to tame foxes, to encourage them to feed from the hand or to encourage them close or into houses using food. Urban foxes are wild animals and should be treated as such."
But a council spokesman added: "I understand there is no confirmed record of a fox on human attack in Glasgow in living memory.
"Certainly, it is generally thought that the population has been declining."
Edinburgh City Council said they had received no recent reports of fox attacks on humans. An RSPCA spokeswoman said it was "extremely unusual" for foxes to attack people.