The decision, reflecting a broader deterioration in EU ties with Turkey, aims to punish Ankara for violating Cyprus' maritime economic zone by drilling off the divided island. It follows a separate decision to stop new arms sales by EU governments to Turkey over Ankara's Oct. 9 incursion into Syria.
Turkey, which is a formal candidate to join the EU, says it is operating in waters on its own continental shelf or areas where Turkish Cypriots have rights.
EU ministers said in a statement that Monday's decision: "will make it possible to sanction individuals or entities responsible for or involved in unauthorised drilling activities of hydrocarbons in the Eastern Mediterranean."
Two EU diplomats said the staggered approach gives Turkey a chance to end what the EU says are "illegal" drilling activities before any measures enter into force.
If sanctions are imposed, the asset freezes and travel bans are likely to target the Turkish military and captains of the drilling ships, the diplomats said.
Cyprus was divided in 1974 after a Turkish invasion triggered by a brief Greek-inspired coup. Several peacemaking efforts have failed and the discovery of offshore resources has complicated the negotiations.
EU ties with NATO-ally Turkey have meanwhile worsened after years of stalemate on Ankara's bid to join the world's biggest trading bloc.With Turkish President Tayyip Erdogan's crackdown on dissidents and his sweeping new presidential powers that the EU says lack checks and balances, many EU states say Turkey no longer meets the democratic criteria to be a candidate, let alone an EU member.