Police said the death of 35-year-old Lynsay Jackson in Kirkcudbrightshire was not being treated as suspicious.
Paramedics attended her home in Crossmichael, Castle Douglas, early today.
Dumfries and Galloway said inquiries were continuing into the circumstances of the death of Mrs Jackson, who it is understood used to run a museum dedicated to her brother's successful racing career in their home town of Twynholm.
Mrs Jackson, who had an eight-month-old daughter, married Will, 34, an environmental health officer at Dumfries and Galloway Royal Infirmary, in August 2011.
Coulthard, 41, took part in the live BBC TV show Saturday Kitchen this morning. It is thought that news of his sister's death was broken to him afterwards.
Their parents, Joyce and Duncan Coulthard, who still live in Twynholm, are flying home from Australia where they have been on holiday.
Until his retirement Mr Coulthard, 67, ran a transport firm, which is now managed by his other son, also Duncan, 44.
Coulthard made his Formula One debut in 1994 and won 13 Grands Prix before retiring from the sport several years ago. He has since provided race commentary for the BBC.
He has lived for many years in Monaco, but also homes in several European countries and owns a number of luxury hotels.
Two years ago, he carried out the opening ceremony at the Rox jewellery shop in the Argyll Arcade, Glasgow, when his F1 car was a star exhibit.