Mr Koizumi said he would take two weeks off in the first month of his child's life. The baby is due later this month.
It will be the first time a Japanese cabinet minister has taken paternity leave.
In Japan, both men and women are entitled to take up to a year off work when their child is born.
But only 6% of fathers did so in 2018 because of pressure to continue working. The figure for women was 82%.