The letter, from a group of female academics and politicians, questioned whether Social Democrat leader Sigmar Gabriel would be able to juggle both roles successfully.
But Gabriel, who is soon due to become a father for the second time, told the Süddeutsche Zeitung on Wednesday he was not impressed.
“Even in this digital age, there are such things as manners,” he said, adding that he would only answer letters sent to him personally before being published.
And in any case, he said, he "discussed private life plans with my wife" and it was no-one else's business.
The ten women wanted to draw attention to the pressure put on women regarding their decisions on combining parenthood and career, the paper said.
Last year Gabriel's party colleague Andrea Nahles was subjected to intense attention when she returned to work two months after having a child. She said she received letters accusing her of being a bad mother fixated on her career.
Family Minister Kristina Schröder also faced similar questions over her choices after having a baby last year, the paper said – yet when the then state premier of Lower Saxony Christian Wulff became a father in 2008, hardly anyone asked if he would be able to continue working.
Anna-Katharina Meßmer, an academic involved in organising the letter, said the aim was to show how unfair the situation was. “It is no women versus men thing,” she told the Süddeutsche Zeitung.
“It simply annoys us that the sole responsibility is foisted onto us women.”
The letter called on Gabriel to set a good example and demonstrate a family partnership in public.