The nine-month-old girls, Lola and Isabella Koupparis, were attacked on Saturday evening as they were sleeping in their cots in Homerton, east London.
One of the twin girls mauled in an apparent fox attack has been transferred to a specialist children's hospital for further treatment on her injuries, doctors said on Tuesday.
Both babies suffered arm wounds and one of them, Lola, also has facial injuries, police said on Monday, APF reports.
The twins were attacked as they slept in an upstairs bedroom at their home in Homerton at around 10pm on Saturday. Their four-year-old brother, Max, who was also sleeping upstairs, was not hurt.
The fox is thought to have crept in through a door on the ground floor which had been left open because of the hot weather while Mrs Koupparis and her husband Nick watched Britain's Got Talent on television, The Press Association reports.