The 43-year-old was held after the bodies of a girl aged four and two boys aged three were found in a large semi-detached house in New Malden, south London, last night.
Police are not looking for anyone else in connection with the deaths of the youngsters, who were pronounced dead at the scene.
Scotland Yard said the woman was taken to hospital for treatment to minor injuries before being discharged and arrested.
A neighbour, who did not wish to be identified, said the three younger children who lived at the house were suffering from genetic disorders - believed to be life-limiting - but an elder child, thought to be around seven or eight years old, was in good health.
She said the family, originally from South Africa, were “really, really lovely people” who moved into the suburb of New Malden with the children a year ago.
The parents, named locally as Tania and Gary Clarence, were “a very, very lovely couple”, the neighbour said, adding: “I saw them all the time about with their children.”
She said the father works in the City and the mother is a full-time carer for her children.
They moved into the house after it underwent a “massive” refurbishment, including the installation of a lift.
“They are very nice people and very, very decent. She is such a lovely person - her life revolves around the children,” the neighbour said.
She said the family have a nanny and help from carers.
A Scotland Yard spokesman said: “A 43-year-old woman has been arrested on suspicion of murder and remains in custody. We are not looking for anyone else in connection with this incident.”
The woman is in custody at a south London police station. The force has given no cause of death but post-mortem examinations will be carried out in due course.
Officers were standing on the doorstep of the address this morning.
Scenes-of-crime officers were earlier seen leaving the property in Thetford Road, carrying evidence bags.
Ethel Winstanley, who lives opposite the couple, said she met the family last summer and congratulated them on the “transformation” of the house after its refurbishment.
“The man was called Gary, that is all I know. We went across to say ‘Congratulations, you have made the street look wonderful’.”
Another neighbour, who did not want to be named, said she met the couple a fortnight ago at a barbecue in the neighbourhood.
“They were very friendly. He played golf and he had been playing golf that morning.
“He was going to America for a golf championship, to watch.
“We were out last night dancing and when we came home there were police cars and ambulances outside.”
Retired nurse and health visitor Joy Devis, 86, said she knew the family and had been in the house “once or twice”.