Endo is the fifth person to leave Abe's cabinet, besides those removed in the reshuffle, since Abe took the premier's seat nearly a year ago.
"The minister has resigned," said a farm ministry spokesman after outgoing Takehiko Endo met Abe.
Endo is to speak at a press conference to be held shortly.
Endo, who took office only on Monday last week in the reshuffle, admitted to two misdemeanours involving government aid and political funding that came to light soon after he started his job.
The disgraced minister initially vowed to stay on, but he decided to step down amid a growing expectation that the new opposition-controlled upper house of parliament will make a censure motion.