Kenya Akiba, who is under fire over alleged illegal political payments to his aides, wife and mother, told reporters: "I believe there is no illegality in terms of my actions."
But "it is not my wish to see proceedings for the budget and other legislative agendas stall", he added.
Shortly after Akiba's resignation, a controversial ruling party member serving as a parliamentary vice minister for internal affairs and communications also stepped down.
Mio Sugita, a right-wing politician frequently accused of divisive rhetoric, has come under fire in recent weeks over comments she made several years ago about same-sex couples and ethnic minorities.
The resignations come as Kishida battles some of the lowest approval ratings of his tenure, with local media describing a "domino effect" of departures from his cabinet.
The public has become increasingly disillusioned after a string of scandals involving ministers and revelations about ties between lawmakers and the Unification Church sect.
"I feel responsible that a minister has resigned," Kishida told reporters after Akiba's departure.
"We must continue to deal with a mountain of tasks at hand. I want to fulfil my responsibility by continuing the work of politics."
Kishida's minister for internal affairs resigned last month over alleged campaign finance irregularities, and his justice minister stepped down in November after reportedly saying his "low-profile" job only generated media coverage when approving death sentences.
In October, the minister for economic revitalisation resigned over allegations of ties to the Unification Church.
The sect has been in the spotlight since reports emerged that the man accused of killing former prime minister Shinzo Abe in July resented the organisation over donations his mother made that bankrupted the family.
The church, officially known as the Family Federation for World Peace and Unification, has denied wrongdoing.
Approval ratings for Kishida's cabinet have been hovering near the so-called "danger level" of 30 percent, and there has been speculation he could reshuffle his cabinet before the next parliament session opens in January.
Kishida said he had no immediate plan to reshuffle his cabinet.