President Michel Aoun said any activity in the disputed area would amount to an act of aggression and a provocation, after the arrival of the natural gas storage and production ship operated by London-based Energean ENOG.L.
Israel says the field in question is within its exclusive economic zone, not in disputed waters.
But in a statement, the Lebanese presidency said Aoun discussed with caretaker Prime Minister Najib Mikati the vessel's entry "into the disputed maritime area with Israel, and asked the Army Command to provide him with accurate and official data to build upon the matter".
Aoun said negotiations to delineate the southern maritime border continued and "any action or activity in the disputed area represents a provocation and an aggressive action".
There was no immediate response from the Israeli government to Aoun's statement. Israeli Energy Minister Karine Elaharrar welcomed the vessel's arrival and said she hoped it would be brought online quickly.
"We will continue to work to diversify the energy market and maintain stability and reliability," she said.
Energean said its floating production storage and offloading vessel arrived on Sunday at the Karish field, about 80 km (50 miles) west of the city of Haifa, in Israel's exclusive economic zone. The company said it planned to bring it online in the third quarter.
Mikati said Israel was "encroaching on Lebanon's maritime wealth, and imposing a fait accompli in a disputed area", calling this "extremely dangerous".