Officers identified the woman as 48-year-old Eva Kemeny and said her body was found after police conducted a search of the five-storey house she shared with her husband at Cadogan Place in the wealthy London borough of Chelsea following the man's arrest.
Metropolitan Police detained the man at a south London police station on suspicion of possession of drugs and also in connection with the death.
Officers from the Homicide and Serious Crime Command were investigating, and the death was being treated as unexplained, police said in a statement.
The man, reported to be Tetra Pak heir Hans Kristian Rausing, later left the station in order to receive medical attention, according to the statement.
Eva's family said they were "deeply saddened by the death of their beloved daughter," in a statement issued Tuesday.
"Eva was a devoted wife for 20 years and mother of four much-loved and wonderful children," it continued.
"During her short lifetime she made a huge philanthropic impact, supporting a large number of charitable causes, not only financially, but using her own personal experiences."
She is the daughter of a wealthy Pepsi Cola executive whose family live on an exclusive island off the South Carolina coast.
Rausing and his wife, who met in a US addiction clinic, spent much of their time in Barbados, where they owned an 11-bedroom mansion.
The Rausing family also released a statement, saying they were "deeply shocked and saddened to hear of the tragic death of their daughter-in-law."
Mr Rausing's cousin, Kirsten, said the news was "very, very tragic".
"Drugs are evil," the Daily Telgraph quoted her as saying. "They have been a problem for Hans and his wife for many years, but I am certain Hans Kristian had nothing to do with her death."
The family, headed by Rausing's father Hans, is worth 4.3 billion pounds, according to this year's Sunday Times Rich List.
Owner Hans, 86, moved to England in 1980 in order to avoid Sweden's high tax rates and lives with his wife Marit on a vast estate in East Sussex, south England.
Hans Rausing and wife Eva were charged in 2008 after she tried to take crack cocaine and heroin into the US embassy in London.
Police later searched the couple's house where they found crack cocaine, heroin and cocaine.
Although they were initially charged with drugs offences, prosecutors subsequently decided to drop the charges and instead give them a conditional police caution. This means they admitted possessing the drugs.
Charity Action on Addiction, which the Rausings supported, said it was "devastated to hear" of her death.
"Without any desire for public recognition, Eva has, through her wonderfully generous support of this and other charities helped so many people for over 20 years. We offer our deepest sympathy to Eva's family at this time of great loss," said a spokesman.