Ferdi Sabit Soyer's resignation followed a decision on Friday by his centre-left Republican Turkish party to part ways with its coalition partner, the centre-right Democrat party.
The two parties have been at odds over efforts to reunify the eastern Mediterranean island.
After submitting his resignation to Mehmet Ali Talat, the Turkish Cypriot president, Soyer said: "There were problems in the coalition. We tried to solve them, but failed."
The Democrat party led by Serdar Denktash, the son of former Turkish Cypriot leader Rauf Denktash, follows a more nationalist line than Soyer's - in refusing to make concessions to the Cypriot government.
Soyer's coalition came to power in May 2005.
Talat is widely expected to nominate Soyer as prime minister-designate as the Republican party holds half the 50 seats in the parliament of the self-proclaimed Turkish Republic of Northern Cyprus (TRNC).
The political crisis comes at a time when Turkey, the only country to recognise the TRNC, is under pressure to resolve a trade dispute over Cyprus or risk jeopardising membership talks with the European Union.
Brussels is demanding Ankara open its air and seaports to Cyprus, a member of the EU, but Ankara has insisted that Greek Cypriots would remain barred unless international restrictions imposed on the TRNC are lifted.
Turkey refuses to recognise the Republic of Cyprus until a viable settlement is reached on the island.
Turkey is the only country to recognise the TRNC.
The Greek Cypriot-led government of the Republic of Cyprus has international recognition and joined the European Union in May 2004.
In June, Tassos Papadopoulos, Cyprus' president and Talat agreed to begin a process under which technical committees would seek to resolve day-to-day community issues, while at the same time tackling more delicate core questions.
The islands have been split since the Turkish invasion of the north in 1974 in response to a Greek Cypriot coup aimed at uniting the island with Greece.