The 43-year-old was held after the bodies 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 their deaths.
A neighbour, who did not wish to be identified, said the three younger children who lived at the house, four-year-old twin boys and an older girl, were suffering from genetic disorders - believed to be life-limiting - but the 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 suburbs of New Malden with their four children a year ago.
The parents, understood to be 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 about a year ago 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.
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'."
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 was being held for questioning in a south London police station.
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.
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."
Two teddies, bouquets, pot plants and a child's skipping rope were laid on the driveway of the house by a police officer.
Investec Bank, where Mr Clarence works as the director of investment banking for healthcare, said in a statement that the firm's thoughts are with him.
It said: "Gary Clarence is a valued colleague and has worked with us for many years.
"We do not know the facts at this time but our thoughts are with the Clarence family.
"We are doing all that we can to help Gary and his eldest child and ask that their privacy is respected."
Investec is an international banking and asset management firm which provides financial products and services mainly based in the UK, South Africa and Australia.
According to the company's website, Mr Clarence leads a team of five corporate broking specialists who advise clients on buying and selling companies, raising money and strategic reviews.
Mr Clarence qualified as a solicitor at Stellenbosch University in South Africa and practised law before moving into the world of business and finance, according to the website.
He completed an MBA at the acclaimed Netherlands Business School, based at Nijenrode University - the only private university in the Netherlands - and joined Investec in 1999.
He spent a couple of years working in corporate finance for the firm and was based in their US office for 18 months, before returning to the UK, where he has specialised in the healthcare sector since 2004.