Yuko Obuchi, daughter of a former prime minister, has been viewed as a possible contender for prime minister.
She said at a news conference that the investigation into the allegations would interfere with her duties as minister of economy, trade and industry. The duties include overseeing the cleanup and decommissioning of the wrecked Fukushima Dai-ichi nuclear power plant.
"I take seriously the impact I have caused," Obuchi said. "My heart is pained by this."
Obuchi's resignation is the first for the current administration of Prime Minister Shinzo Abe and could dent his efforts to raise the profile of women both in politics and business.
The questions over Obuchi's use of election funds are the latest in a series of uproars over activities by some members of Abe's Cabinet. Obuchi is one of five women Abe appointed to Cabinet-level posts in a reshuffle last month that highlighted his commitment to promoting women to leadership positions.
"I apologize for not being able to make any contributions as a member of the Abe Cabinet in achieving key policy goals, including the economic recovery and a society where women shine," Obuchi said.
Abe's justice minister, Midori Matsushima, has been under fire for distributing hand-held fans, called "uchiwa," to supporters, also in possible violation of the Political Funds Control Law.
Since taking office in late 2012, Abe had managed until now not to lose any of his Cabinet members to scandal or other problems. The conservative Sankei newspaper ran a headline recently that read "Government's 'Resignation Dominos' Alert."
Grilled by opposition party members in parliament last week, Obuchi apologized for funding irregularities, though she said she had found no evidence of alleged personal use of campaign funds that were paid to a company run by a relative. Obuchi said neckties and handkerchiefs designed by her sister were used for political activities, as gifts and souvenirs.
All purchases using election funds, including for baby clothes, vegetables and other gifts, were for her political activities such as promoting her home prefecture, not her personal use, Obuchi said.
But discrepancies in the accounting for several years have raised a "major doubt," she said.
"This is my own fault and I will focus on investigating so that I can retain trust from my supporters as soon as possible," Obuchi said.