The EU will halt high-level dialogue with Turkey, suspend talks over an aviation agreement and cut 145.8 million euros ($164 million) in pre-accession financial funds allocated for 2020.
Foreign ministers from the bloc also told the European Commission, the bloc's executive, to keep working on possible financial sanctions targeting those involved in the drilling operations.
And the European Investment Bank has been asked to revisit the conditions set out for providing financial support to Ankara.
The EU last month warned Turkey it could face sanctions if it did not cease what the bloc called "illegal" drilling in Cyprus's exclusive economic zone.
Last week, diplomats began discussing what measures to impose.
It was the discovery of huge gas reserves in the eastern Mediterranean that sparked the dispute between EU member Cyprus and Turkey.
Ankara sent two ships to carry out drilling off the Cypriot coast despite the warnings from the EU.
Cyprus has been divided between the Republic of Cyprus and a northern third under Turkish military control since 1974 when Turkey invaded in response to a coup by a Greek military junta.
The tensions over gas drilling are also likely related to the collapse of peace talks in 2017, experts say.
While negotiations to reunify the island have not restarted, Cyprus has moved to start gas and oil exploration by issuing licences.
