 "Japan industry minister resigns over make-up scandal: Reports")
Yuko Obuchi, who had been tipped to potentially become the country's first female prime minister, handed Abe her letter of resignation during a 30-minute meeting with the premier, public broadcaster NHK and Jiji Press news agency said.
Abe accepted her resignation, according Jiji.
Obuchi said she would hold a news conference soon. She would be the first minister to resign since Abe took power in December 2012.
Obuchi was a star minister when Abe reshuffled his cabinet in September, becoming the country's first woman in charge of economy, trade and industry - a powerful portfolio that includes oversight of the energy sector.
The clean-cut 40-year-old was the most prominent of a new wave of women promoted to leading Cabinet positions.
But she is now facing claims that, over the five years to 2012, her political funding body spent more than 10 million yen ($95,000) on things unconnected to politics, including cosmetics and accessories at a department store.
Her political group has also invited residents in her electoral district in central Japan on bus tours to see theatre performances in Tokyo at fees below actual costs - a move opposition lawmakers have called 'vote-buying".