David Clapham, head of special business units, is also leaving. He has been with the company for 35 years, but Sainsbury's announcement misspelled his name.
Ms Thorne, 47, at Sainsbury's for seven years, is one of few female executive directors of a FTSE 100 company. She is leaving by mutual consent "to pursue other opportunities", but will be eligible for substantial compensation. Ms Thorne was on a two-year contract and earned a total of pounds 426,000 last year. It is thought her pay-off will be less than pounds 400,000.
Sainsbury's said her departure was due to the separation of finance functions between the group and the Sainsbury's supermarkets board.
Her departure is not a surprise as the City has known for some time that Sainsbury's has been keen to appoint a more powerful finance director. Several candidates are thought to have been offered the job last year.
"I think they needed a stronger personality in that job, though it is not fair to blame Sainsbury's problems on her," one analyst said.
Mike Dennis at SG Securities added: "You have to ask whether this really changes anything in the business. The key people behind their strategy - which has not exactly covered itself in glory - are still there."
Sainsbury's is now looking for a replacement but would not say if an internal appointment was possible. The company is backing its marketing director, Kevin McCarten, who has been criticised after the unsuccessful "Value to Shout About" advertising campaign starring John Cleese. In the new board he has been given extra responsibility for brand development.
The shares fell by 0.25p yesterday to 380.75p.