The animal seriously injured the infant after entering his bedroom in Bromley, south east London, according to reports.
The child’s mother was alerted by his screaming and rushed into his room to see his hand lodged “halfway down the animal’s throat”, the Mail on Sunday said.
Surgeons were able to reattach the baby’s finger and he was said to be recovering well.
A Metropolitan Police spokesman said investigations were continuing after officers were called last Wednesday by staff at St Thomas’s Hospital to reports a baby boy had been admitted to hospital after being attacked by a fox.
London mayor Boris Johnson said more must be done to tackle the growing problem of urban foxes.
He told BBC News: “They may appear cuddly and romantic but foxes are also a pest and a menace, particularly in our cities.
“This must serve as a wake-up call to London’s borough leaders, who are responsible for pest control. They must come together, study the data, try to understand why this is becoming such a problem and act quickly to sort it out.”
Mr Johnson also said his thoughts were “with the baby boy and his family”.
An RSPCA spokeswoman said the only reason a fox would attack is due to fear.
She said: “It’s extremely unusual for foxes to attack young children or anyone.
“It’s not typical fox behaviour at all. Foxes will come closer to a house if there are food sources. Then they can become quite bold, but they usually do back off and run away when there’s people around.”
The issue of foxes attacking humans has divided the public, with many sceptics questioning recent cases amid fears of a backlash against urban foxes.
In April last year wildlife presenter Chris Packham said he simply did not believe reports of people getting attacked by the animals.