Matthews has been with the company for five years and will leave the supermarket group at the end of its financial year, in March 2005.
His announcement comes two weeks before Justin King, Sainsbury’s chief executive, is to announce the results of his strategic review.
Analysts have raised their concerns that the company will issue another profits warning on this date, according to newspaper reports today.
Matthews exit follows that of Lord Levene and Keith Butler Wheelhouse who both quit their roles as non-executive directors last month. Sir Peter Davis, the former chief executive, left in July, while Stuart Mitchell (former head of supermarkets, Sara Weller (former deputy managing director) and Keith Evans (former head of non-food) also left earlier this year.