The opinion piece, published by the Xinhua news agency, said Ms Tsai did not have the "emotional burden" of a family, leading to an "erratic style".
Chinese social media users largely rallied in support of Ms Tsai, who has been outspoken about her single status.
She was sworn in on Friday as Taiwan's first female president
Tsai Ing-wen, Taiwan's shy but steely leader
Taiwan: the place to be a woman in politics
Her Democratic Progressive Party (DPP), which leans towards independence from China, won January's elections, ending eight years under pro-Beijing President Ma Ying-jeou.
Ms Tsai's singleness was a central focus of a commentary by Wang Weixing, originally published by Xinhua.
The article has since been removed from Xinhua's website, but can still be found on other news portals and micro-blogging accounts.
Mr Wang, a senior military officer, pointed to an "extremist political-style development" displayed by Ms Tsai.
"As a single female politician, Tsai Ing-wen does not have the emotional burden of love, of 'family' or children so her political style and strategies are displayed to be more emotional, personal and extreme," the report in Chinese read.
It continued that her "erratic behaviour" influenced her political style and advised that she should take that into consideration, rather than "focus on long-term goals" for Taiwan.
Alex Huang, a spokesman for Ms Tsai, told BBC News that her office had "no comments" in response to the piece.