The ministry stressed that Cyprus' membership in the European Union did not mean that the island's Greek community could "usurp the legal rights and interests of Turkish Cypriots".
Turkey contests the rights of Cyprus to explore for gas, sending its own drilling ships to stake claims around the island. A second vessel, Yavuz, has now sailed to an area off the Karpas peninsula on Cyprus' east coast.
Cyprus has been split between a Turkish Cypriot north and Greek Cypriot south since 1974 when Turkey sent troops to the island in response to a Greek military coup.
Reportedly the European External Action Service would also advise member states to refrain from high-level contacts with Turkey.
The Greek south has worldwide recognition while only Turkey recognizes the government in the north. Turkish Cypriots claim most of seven blocks in the east.
Meanwhile, the Greek Cypriots have signed EEZ agreements with Egypt, Lebanon and Israel to which Turkey has objected on the grounds, it says, that certain areas in Cyprus's EEZ, fall under the jurisdiction of Turkey or of the Turkish Republic of Cyprus. Several peacemaking efforts have failed and the discovery of offshore resources has complicated the negotiations. Cyprus says Turkey is encroaching in waters where the country has exclusive economic rights while the European Union warned Turkey of sanctions.
On Tuesday, the Egyptian foreign ministry said Turkey's intention to drill "represents a continuation of unilateral measures that serve to increase tension in the Eastern Mediterranean region", stressing the need to avoid escalation.
"We express our deep concern over Turkey's attempt to conduct a new drilling operation in the northeast of Cyprus".