Koizumi said he hopes to inspire further debate on how to balance work and family duties, including care for children and the elderly, in a sustainable way.
Koizumi said in the prime minister's office that he had participated in the delivery and that both the mother and baby were doing well.
The 38-year-old politician earlier said it was a hard decision, but that he was going ahead with the plan to pave the way for other male employees in his ministry and working fathers elsewhere.
Japan has relatively generous parental leave policies, allowing men and women partially paid leave of up to a year. However, very few men take advantage of the perk. "They want to take the leave, but it's hard", he wrote then.
Young male workers, however, appear to be keen to change the trend.
Men likely fear losing their jobs if they take paternity leave - and have good reason to.
The government's top spokesman backed the move, saying it was "important to create a conducive work-place atmosphere and social acceptance and support for men to ask for and take parental leave".
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According to Komuro, the most common cause of death in mothers soon after giving birth is suicide linked to postpartum depression.
Mr Koizumi said he would take two weeks off in the first month of his child's life.
The telegenic Koizumi, popularly known as Shinjiro to distinguish him from his father, grabbed headlines in the summer of 2019 with news he was marrying Christel Takigawa, a French-Japanese television personality, and that they were expecting a child.
Koizumi is the son of former hipster prime minister Junichiro Koizumi and is considered a future prime minister with hope.
His plan has sparked reactions, both positive and negative, in political circles and online. Others welcomed his decision as the beginning of change.
As per a 2018 UNICEF report, almost two-thirds of the world's children under 12 months come from countries where fathers are not entitled to paid paternity leave.
But opposition lawmaker Kenta Izumi of the Democratic Party for the People has not seen such moves favorably.
"I hope my taking paternity leave will lead the way of working styles to one where everyone can easily take child-care leave without hesitation in the environment ministry", Koizumi told his staff, according to the Times. Kendanren is Japan's most powerful business lobby group for major companies.