The lawmaker denies the allegations of anti-Semitism and homophobia, saying his social media accounts had been tampered with and most of the alleged postings falsified.
The affair is an unwelcome distraction for the Tsipras as he grapples with the tasks of meeting the terms of Greece's latest 86 billion euro ($97 billion) bailout and dealing with tens of thousands of people arriving on Greek shores in Europe's biggest refugee crisis since World War Two.
Tsipras, who made the appointments on the recommendation of his coalition partner, appeared oblivious to the minister's reputation for controversial comments -- the lawmakers was lambasted by Jewish organisations in the summer for comparing Greece's economic predicament to Auschwitz.
"Everyone on Twitter knew about Kammenos except Tspiras," the centre-right Eleftheros Typos newspaper said on its front page on Thursday.
Tsipras eventually told his coalition partner that Kammenos should explain himself after news of a social media storm reached him in Brussels, where he was representing Greece at a summit on the migrant crisis.
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"It shows inattention to detail, insensitivity, especially if they knew about it. And it shows that to err is human, but to err twice is stupid," said political analyst Theodore Couloumbis.
In July Tsipras parted company with Yanis Varoufakis, the combative academic he had appointed as finance minister, after Varoufakis repeatedly infuriated international lenders in talks over Greece's debt mountain.
That resignation and the subsequent bailout agreement exposed fissures in Syriza, culminating in a split that triggered a snap parliamentary election.
"Whether it was ignorance, or they were aware of it, it's inconceivable to appoint such a person to the government," veteran leftist Panagiotis Lafazanis told Reuters, referring to Kammenos' appointment.
"Citing ignorance is simply not justified," said Lafazanis, who is head of the Popular Unity party that broke away from Syriza last month.
A Syriza insider said it was all down to politics.
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"There is not an issue with Tsipras's judgment...It is about keeping a balance with your partner in government," the party official told Reuters, declining to be named.
To illustrate the point, the official said Tsipras had rejected another person from the Independent Greeks' list.
Couloumbis said Tsipras had made some good choices too, such as the reappointment of Finance Minister Euclid Tsakalotos and his deputy, George Chouliarakis.
"It's not fair to just talk about the banana peel he just stepped on without mentioning the right choices," he said.