Greek Prime Minister Alexis Tsipras has said he will call a confidence vote after his governing coalition split over the Macedonia name change.
Defence Minister Panos Kammenos withdrew his party's support, signalling his opposition ahead of an expected vote in the Greek parliament.
The two countries recently agreed that Greece's northern neighbour would be called North Macedonia, therefore ending a 27-year-long row.
Macedonia has ratified the deal.
Greek nationalists argue that the name “Macedonia” can only refer to the Greek province of the same name.
The dispute, which has raged since it voted for independence from Yugoslavia in 1991, is blocking Macedonia's hopes of joining Nato and the European Union.
Where does this leave Greece?
Following the resignation of Mr Kammenos, Mr Tsipras said he was moving immediately to a confidence vote, which is expected on Wednesday, according to Greek newspaper Kathimerini.
The Syriza party of Mr Tsipras has 145 seats in the 300-seat parliament and Mr Kammenos has called on his Independent Greeks (Anel) party, which has seven, to vote against…