"We are very concerned that members of Hezbollah do possess Venezuelan passports. We are investigating this matter very, very closely", the official told reporters.
The United States has designated Hezbollah as a terrorist organisation and considers it to be a regional proxy of Iran.
Earlier the same day, the US government sanctioned two Venezuelan officials - Gustavo Adolfo Vizcaino Gil and Juan Carlos Dugarte Padron - under the Global Magnitsky Act.
The Treasury Department official also said that designating Gil and Padron did not imply they provided passports to Hezbollah members.
Hezbollah emerged in the 1980s as a Shiite paramilitary organisation aimed at ending Israel's occupation of southern Lebanon. It later evolved into a political party that currently has representatives in the country's Cabinet, Parliament and municipalities.