But he ruled out resigning after it emerged ministry officials had removed hundreds of references to Abe, his wife, and Aso from documents related to the sale of state land at below-market prices.
"I am voluntarily returning 12 months of my salary as a cabinet minister, as this problem has hurt public confidence in the finance ministry and the administration as a whole," Taro Aso told reporters, Presstv Reported.
But he added, "I am not thinking about stepping down", as he announced the findings of the ministry's in-house probe.
Aso is the richest minister in Abe's cabinet because of his family's massive fortune made in the mining business. He also earns some 30 million yen ($274,000) a year as a cabinet minister.
Aso said the ministry had penalized around 20 officials, imposing pay cuts in some cases and issuing verbal reprimands to others.
"Officially approved administrative documents should never have been altered and submitted to parliament. I find this extremely regrettable," he said.
Abe told reporters he wanted Aso to stay on to ensure lessons were learned from the scandal.
"We should conduct a thorough review of how to keep public documents and take measures to prevent a recurrence," he said, adding that he wanted Aso "to take leadership in this and fulfil his responsibility."
The scandal revolves around the 2016 cut-price sale of state-owned land to a nationalist school operator who claims ties to Abe and his wife Akie.
The penalized officials include Nobuhisa Sagawa, whose office helped alter key documents related to the controversial land sale. He has since resigned.
Giving sworn testimony in parliament soon after he quit the ministry in March, Sagawa denied any involvement by Abe or the prime minister's office in falsifying the documents.
But the senior bureaucrat declined to answer detailed questioning about how and when documents were altered, saying he was under criminal investigation.
Prosecutors last week decided not to press charges against him.
Abe also faces a second cronyism scandal in which the opposition alleges he used his influence to help an old friend open a school in a special economic zone, bypassing cumbersome government regulations.
Abe, in power since late 2012, is in no imminent danger of losing his job, but the scandals have affected his popularity.
A new opinion poll released Monday showed voter support for his cabinet down 1.6 percentage points over the past month to 39 percent, the lowest level since he took office.
The finance ministry, considered the most powerful in Japan's bureaucracy, has also been rocked by a sexual abuse scandal that forced the resignation of a senior official.