She was also banned from driving for 13 months after appearing at Oslo City Court.
Andresen was found to be three times over the legal limit when she was breathalysed more than an hour after being stopped, according to Norwegian newspaper VG.
She was handed a suspended prison sentence of three weeks and told financial newspaper Finansavisen that she had believed herself to be under the blood alcohol level of 0.02.
"I thought I had waited long enough not to be over the limit any more," she said. "I am very sorry."
Her family's fortune stems from its purchase of Norwegian tobacco firm JL Tiedemanns Tobaksfabrik in 1859.
In 2004, a Norwegian woman was fined a record 500,000 kroner (NZ$73,630) for drink-driving, according VG.
She had drunk up to 11 glasses of wine in a bar in the country's capital before driving off and hitting three parked vehicles in just 100 metres of road.
The country's legal limit of 0.02 is one of the strictest in Europe, with the legal limit in England, Wales and Northern Ireland set at 0.08.