Lynsay Jackson, 35, was discovered at her home near Dumfries in Scotland this morning.
Mrs Jackson, who has an eight-month-old daughter, ran a museum dedicated to Mr Coulthard's sporting achievements in his home village of Twynholm, Kirkcudbrightshire. She also previously ran his fan club.
A Dumfries and Galloway Police spokesman said enquiries were continuing but her death was not believed to be suspicious.
Mr Coulthard, 41, appeared on the BBC One cooking programme Saturday Kitchen this morning. It is understood that news of his sister's death was broken to him after the live show.
Their parents, Joyce and Duncan Coulthard, who still live in Twynholm, are flying home from Australia where they were on holiday. Until his retirement Mr Coulthard, 67, ran a transport firm, which is now managed by his other son, who is also called Duncan, 44.
Mrs Jackson married Will, 34, an environmental health officer at Dumfries and Galloway Royal Infirmary, in August 2011.
One friend of the family who lives in Twynholm said: "It's a terrible shock for everyone. She was so well-known as are the family. It's a really sad day for everyone."
A Dumfries and Galloway Police spokesman said: "We can confirm that a 35-year-old woman was found dead in her home today in Crossmichael.
"Our enquiries into her death are ongoing at this time but there are not believed to be any suspicious circumstances and a report is being prepared for the procurator fiscal."
Mr Coulthard, 41, made his Formula One debut in 1994 and had 13 Grand Prix victories in a career which spanned 15 seasons. In 2001 he came second in the drivers' championship.
After retiring from Formula One he became a BBC commentator and pundit.