NHS Grampian has apologised to the parents of the young patients at Denburn Medical Practice.
It is believed the fridge could have been malfunctioning since last October.
The health board said it did not foresee any health problems arising from the situation.
Dr Diana Webster, consultant in public health medicine, said: "Our concern is that the effectiveness of the vaccines may have been compromised so they may not provide the necessary long-term protection.
"The expert advice we received was that boosters should be offered as a precautionary measure, and we can reassure parents there is no risk from the additional dose of vaccine."
The families of more than 50 babies and young children in Aberdeen are being offered revaccinations after the fridge the original doses were kept in was found to be faulty.