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The body of Eva Rausing, a member of the family behind the Tetra-Pak drink cartons empire, was reportedly found in a home in London, according to the BBC.
She was one of the UK's richest women.
A 49-year-old man had been arrested in connection with the woman's death and on suspicion of possession of drugs, a Metropolitan Police spokesman said. The death is being treated as unexplained.
Mrs Rausing, 48, is the wife of the heir to the £5.4bn Tetra Pak fortune, Hans Kristian Rausing, 49. In 2008 the couple were in trouble with the police over drugs but the prosecution was formally discontinued.
A spokesman for the Metropolitan Police told Sky News:
"Yesterday (Monday) a 49-year-old man was arrested on suspicion of possession of drugs.
"Following a subsequent search of an address in Cadogan Place in SW1 a body was found.
"The death is being treated as unexplained and a post-mortem examination began at 1pm today at Westminster mortuary.
"We believe we know the identity of the deceased but we are awaiting confirmation.
"The 49-year-old man was further arrested in connection with the death and is in custody."
The couple have four children.
Last Updated (Tuesday, 10 July 2012 19:01)