The death comes less than months before an election for parliament's upper house, a key test for Abe's leadership.
Matsuoka, 62, was found unconscious in his room at a residential complex for legislators near parliament in the centre of the Japanese capital.
He was then taken to hospital where he was confirmed dead, Japan's chief cabinet secretary told reporters.
Media reports have linked Matsuoka to a number of political fund scandals, including a case in which he had declared substantial office expenditures when his office was in fact rent-free.
Last week, media said the minister had received political donations from businessmen involved in a bid-rigging scandal.
Matsuoka has repeatedly denied any wrongdoing.
Support for Abe's cabinet has plunged to 32 per cent, down 11 percentage points from a similar poll in April, according to a weekend survey by the national Mainichi Shimbun newspaper.
A separate poll by the Nikkei business daily showed Abe's popularity falling to 41 per cent, down 12 percentage points from the previous month.
Both polls cited dissatisfaction with the government's apparent loss of pension payment records for millions of people.