Mr Tsipras's party has 145 seats in the 300-seat Parliament.
He said his party is quitting the government.
Macedonia was founded in 1991 and recognized by the United Nations in 1993, but was accepted to the United Nations membership with the name of Former Yugoslav Republic of Macedonia (FYROM) due to Greek objection to the name Macedonia.
The impact of the resignation on the governing coalition was not immediately clear. However some of his ANEL party's MPs remain ambivalent.
In June 2018, Greece and Macedonia inked Prespa Agreement, which requires Macedonia to change its name to the Republic of North Macedonia and Greece to drop its objection to Macedonia joining the North Atlantic Treaty Organization (NATO) and becoming a member of the European Union.
Prime Minister Alexis Tsipras continues to declare his belief that the deal will be ratified with the support of a few centre-left and independent lawmakers, filling in for the loss of ANEL support.
Greece's government unraveled, prompting Prime Minister Alexis Tsipras to call a confidence vote that could trigger an early election and end the leftist leader's four years in power.
Kammenos, who forged a coalition pact with Tsipras in 2015, never concealed his hostility to the deal with Skopje, which renames the tiny Balkan country Republic of North Macedonia.More news: Chris Pratt announces engagement to Katherine Schwarzenegger
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Tsipras said he had a "frank discussion" with Kammenos, whom he thanked for his government partnership, and announced that Admiral Evangelos Apostolakis, chairman of the Joint Chiefs of Staff, will become the country's new defence minister.
Tsipras has said that the chamber would be asked to ratify the agreement with Macedonia by the end of the month.
Kammenos has long opposed the accord with neighboring Macedonia signed by their governments previous year.
"Our parliament found the strength but it wasn't easy". He said that he believes he can find the required six votes.
Zaev said on January 12 that the lawmakers had "made history", adding: "I know how hard that was". The controversial agreement would also allow Macedonia to join North Atlantic Treaty Organisation and the European Union.
Kommersant estimates that the adoption of constitutional changes can have another effect, important not only for that Balkan state, adding that "in the opinion of regional experts, this can influence the granting of autocephaly to the Macedonian Orthodox Church".
For the Greeks, Macedonia is the name of a history-rich northern province that was the cradle of Alexander the Great's ancient empire.
New Democracy is vehemently against the agreement but Tsipras hopes to convince opposition MPs from smaller parties to back the historic name change deal.