The young girl was injured by the drug patrol dog in Belmarsh Prison, Woolwich, on 31 March.
The Ministry of Justice (MoJ) said the incident had been reported to police and the dog withdrawn from service.
In 2015, the MoJ said there were more than 530 dogs deployed in prisons in England and Wales.
The Mirror reported the attack had taken place during a routine drugs test and the girl needed to undergo plastic surgery because of her injuries.
The MoJ said it could not release more details because of "purdah" rules in the run up to the general election.
A toddler was bitten by a sniffer dog while she was visiting a relative in a high security jail in east London, it has emerged.