Lola and Isabella Koupparis are said to be in a "serious but stable" condition in hospital, after being mauled on Saturday evening at their home in Hackney, east London.
The nine-month-old girls both suffered arm wounds and it is believed Isabella also has facial injuries.
Their mother Pauline Koupparis described the incident as "like a living nightmare".
She told radio station BBC London: "It's something I would never expect to happen to anybody, let alone happen to my beautiful girls."
Mrs Koupparis had been watching television when she heard the girls crying, she said.
"I went into the room and I saw some blood on Isabella's cot," she said. "I thought she'd had a nosebleed.
"I put on the light and I saw a fox and it wasn't even scared of me, it just looked me straight in the eye."
The infants were covered in blood and crying and she and her husband were "hysterical", she added.
The fox stood its ground even when her husband Nick rushed up to the room, she said.
"The fox didn't even leave the room.
"My husband lunged at it three or four times and he sort of moved a few inches each time."
Eventually the couple managed to chase it off and rang 999.
Both girls have undergone surgery, she said.
Lola, who looked "dreadful" but was doing well, had a number of facial injuries and some puncture marks on her arm and Isabella suffered injuries to her arm and was receiving special care, their mother added.
Police said the girls were in a "serious but stable condition" at the Royal London Hospital.
The fox apparently entered through a door on the ground floor which had been left open because of the heat.
The twins' four-year-old brother, Max, who was also sleeping upstairs, was not hurt.
Michael Parra, 48, a health trainer, who has lived in the street for six years, said police had been going from house to house after the attack, warning residents not to leave their doors open.
He said: "Police told us that in the hot weather we should keep our doors closed for our safety. We see a lot of foxes around here. They're always in our garden.
"Something should be done about them. I would love to get them out of here. They're really a nuisance and a danger."
Hackney Council said this was the first time it had ever had a report of a fox attacking a resident.
But Joe Lobenstein, 83, a former civic mayor of Hackney and ward councillor, said he had warned the council about the dangers of foxes in the area as far back as the early 1990s.
In 2002 Kent woman Sue Eastwood said her baby boy, Louis, was injured after a fox crept into their house while she slept.
Louis, 14 weeks old, suffered bite marks on his head after the animal crept into the sitting room of the house in Dartford.
WILD ANIMALS AT HOME IN TOWN
In Britain, foxes were first seen in cities such as London and Bristol during the 1940s.
Estimates suggest that the UK-wide population is about 258,000, with as many as 10,000 red foxes living in the London area alone.
In Scotland is estimated that there are 23,000 foxes.
Foxes principally come into gardens for food and shelter – householders are advised to make sure they get neither.
One concern about foxes is the possibility of the spread of disease to humans and pets.
Another concern is "mange", caused by mites, which can live on foxes.
Though foxes are native to Britain, during the 1800s foxhunts imported many thousands from Europe to increase numbers in lowland areas.