Rausing, 48, was the wife of Hans Kristian Rausing, heir to the TetraPak fortune his father built by creating a successful manufacturer of laminated cardboard drink containers.
Both Rausing and her husband have had long-running and often public battles against addiction.
British police said they had arrested a 49-year-old man Monday on suspicion of drug possession and a subsequent search of an address in London's tony Belgravia neighborhood related to that arrest turned up Rausing's body later that day.
The man was widely named in the British media but police would not confirm his identity.
Scotland Yard said in a statement Tuesday that further tests were being carried out on Rausing's body after an autopsy was inconclusive. It said officers from the Homicide and Serious Crime division were investigating the case "and the death continues to be treated at this time as unexplained."
The man arrested in connection with Rausing's death remained under arrest but was receiving medical attention at a location away from the police station, police said. They would not say if the man was under guard.
After the news broke, her parents, Tom and Nancy Kemeny, and the rest of her family paid tribute Tuesday to a "devoted wife" and mother of four "much loved and wonderful children," saying they were devastated over her death.
"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," the family said in a statement. "She bravely fought her health issues for many years."
A statement from her in-laws, Hans and Marit Rausing, said they were "deeply shocked and saddened to hear of the tragic death."
Eva Rausing supported a number of charities that helped to fight addictions. One of them—Action on Addiction—was among the first to express sadness over her death and praise her "wonderfully generous" support over the years.
She also was listed as a long-term supporter of The Prince's Foundation, part of a group of nonprofit charities that have Prince Charles as their patron. His office said the prince was told of Rausing's death but did not offer further comment.
In a diplomatic scandal in 2008, Eva Rausing was arrested outside the U.S. Embassy in London for reportedly trying to bring crack cocaine and heroin into building in her handbag. Police later found small amounts of cocaine, crack and heroin in a search of couple's 5 million-pound (then $10 million) London town house. The couple was charged with drug possession but prosecutors later agreed to drop the charges in exchange for formal police warnings.
At the time, the Rausing family issued a statement saying relatives were "deeply saddened" by the couple's drug problems and hoped they could overcome their addictions.
Hans Rausing's Swedish father helped transform TetraPak into a hugely successful manufacturer. The fortune of the senior Rausing and his family is estimated at 4.3 billion pounds ($6.7 billion) by the Sunday Times Rich List.
——— Cassandra Vinograd can be reached at http://twitter.com/CassVinograd