Fox News ridiculed the Transport Secretary, who adopted a daughter and a son with his husband Chasten in August, implying he was "trying to figure out how to breastfeed."
Buttigieg, 39, has been on paid leave since mid-August to spend time with his family.
Though, since then, blockages in ports and a truck driver disaster have caused significant problems in the supply chain, leaving shelves empty and causing shipping costs to rise.
Carlson announced: "As just about every sane person has acknowledged, inflation is rising because the government has devalued the US dollar by making too many US dollars."
"The; they're sand now, they're not worth much. But still the White House does not seem concerned."
"Pete Buttigieg has been on leave from his job since August after adopting a child – paternity leave, they call it – trying to figure out how to breastfeed. No word on how that went."
"But now he's back in office as the Transportation Secretary, and he's deeply amused, he says, to see that dozens of container ships can't get into this country."
The remarks drew criticism online, with some accusing Carlson of homophobia.
Politico on Thursday announced Buttigieg has been on paternity leave since August.
The Transport Secretary's office told them he had been on paid leave since mid-August to spend time with his husband Chasten and their two newborns.
A spokesman announced: "For the first four weeks, he was mostly offline except for major agency decisions and matters that could not be delegated."
"He has been ramping up activities since then."
The spokesman added that Buttigieg would "continue to take some time over the coming weeks to support his husband and take care of his new children."
According to a Thursday report, it comes after Senator Rick Scott called on Buttigieg and Commerce Secretary Gina Raimondo to testify before the Senate Committee on Commerce, Science, and Transportation.
"There is more that the Department of Transportation can and should be doing to help address ongoing supply chain matters related to the pandemic," said Senator Cynthia Lummis.
"We're well over a year into this, and I'm concerned that the Biden administration seems more focused on pushing Congress to massively expand the federal bureaucracy rather than using their existing authorities to help American businesses and consumers get back to normal," the Senate Transportation Committee member continued.
Representative Kevin Brady, the ranking member of the Ways and Means Committee, continued that the administration's actions finally addressing these matters is "months late and more than a dollar short."