The animal seriously injured the infant after entering his bedroom in Bromley, south east London, according to reports.
A Metropolitan Police spokesman said: "We were called at 1638 on Wednesday 6 February by staff at St Thomas's Hospital to reports a baby boy who had been admitted to hospital after being attacked by a fox.
"Police attended to find a four-week-old baby with a hand injury. The baby was admitted to hospital after the attack at its home address in Bromley. Inquiries continue."
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".
Surgeons were able to reattach the baby's finger and he was said to be recovering well.
London Mayor Boris Johnson said more must be done to tackle the growing problem of urban foxes.
He said: "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, in an interview with the Radio Times.
The broadcaster, who gave his views on the back of a Channel 4 programme Foxes Live: Wild In The City, said there was no proof that the creatures attack dogs and cats except in "exceptional circumstances".
Packham said that the urbanisation of the fox was "celebrated" in the late 1960s but "now we've seemingly tired of their antics and we're hell-bent on blaming them for all the crimes we can.
"But their only true crime is ... being too successful and that's another thing we Brits just can't stand," he told the magazine.
"Validated assaults of dogs and cats are non-existent, except under exceptional circumstances.
"And as for attacks on humans - I'll be necessarily diplomatic - I don't believe it."
The fox attack is not the first such incident. Here are details of some other attacks on humans:
:: In June 2010 nine-month-old twins Isabella and Lola Koupparis were savaged by a fox in their cots after it crept into their home in Hackney, east London.
Their parents dialled 999 after finding Isabella with deep cuts to her arm and Lola's face covered in blood.
Both girls were taken to the Royal London Hospital where they were given antibiotics and underwent surgery.
The family underwent counselling to help them come to terms with the traumatic attack.
The case sparked a national outcry as some questioned the couple's story amid fears of a backlash against urban foxes.
:: Later the same month toddler Jake Jermy was taken to hospital after reports he had been attacked by a fox while attending a party at a school in Brighton, East Sussex.
It was understood the three-year-old was bitten on the arm after he stroked the tail of the animal, which was sticking out from under a temporary building and it then turned on him.
:: In September 2003 four-year-old Jessica Brown was also bitten on the arm when a fox crept into her upstairs bedroom in Tufnell Park, north London, while she was sleeping.
:: In July 2002 Peter Day told of how a fox attacked his baby son Louis at his home in Dartford, Kent.
The 14-week-old suffered four puncture wounds on his head and had to be kept in hospital overnight.
Mr Day said: "I came into the living room and there was a fox sitting there beside my wife. He had already done the damage to Louis.
"I picked him up and chased the fox out of the house and all the way up the garden."