Ambassador Ali Awad Assiri told Lebanon's Future TV late on Wednesday that Saudi Arabia will deport "those who financially support this party."
He didn't say when such deportations would begin.
Saudi Arabia is a strong backer of the mostly-Sunni Syrian opposition trying to remove Syria's President Bashar Assad from power.
Assad belongs to the minority Alawite sect, an offshoot of Shiite Islam. Shiite Hezbollah fighters were instrumental in a recent regime victory when government forces regained control of the strategic town of Qusair near the Lebanese border.
There are tens of thousands of Lebanese — including Shiites — working in the kingdom.