The incident sparks new travel warnings as well as a diplomatic complaint to Lebanon from Saudi Arabia.
Hizbollah stops Saudis and Kuwaitis at checkpoints
The two countries reiterated warnings for their citizens to avoid travel to Lebanon and called on those in the country to leave immediately.
Kuwait's embassy in Beirut said its warning came "in the midst of security uncertainty and consequent harassment", adding that a Kuwaiti diplomat had been stopped at a checkpoint "outside the framework of the state".
The statement, reported by the state news agency late on Friday, said that Kuwait had organised a plane for any citizen wishing to leave Lebanon that evening.
Separately, the Saudi ambassador to Lebanon, Ali Asiri, filed a diplomatic complaint with the Lebanese government after several of its nationals were stopped by Hizbollah in a diplomatic car and held in "degrading conditions", the London-based Saudi-owned newspaper Asharq Al Awsat reported yesterday.
The incident happened in Beirut's southern suburbs, a stronghold of the Shiite group, the report said.
Although all six Gulf Cooperation Council states have issued previous travel warnings to Lebanon, the new incidents highlight growing regional tensions over the conflict in Syria, as the United States contemplates military action against President Bashar Al Assad over his alleged use of chemical weapons.
GCC members have been among the strongest regional supporters of the opposition to Mr Al Assad's regime, and last week, the UAE, Saudi Arabia and Kuwait helped sponsor an Arab League resolution blaming the Syrian government for the chemical weapons attack on August 21.
Lebanon is often considered the most fragile of Syria's neighbours and most likely to be consumed by the spillover its two-and-a-half year civil war.
Hizbollah has sent fighters to Syria to join Mr Al Assad's soldiers.
Two recent bomb blasts have also been linked to regional tensions. On Friday, Lebanon charged five men, including a Syrian intelligence operative and a cleric with ties to the Syrian regime, for bomb attacks in Tripoli that left 47 dead.
The GCC travel warnings were echoed by Britain and France, who also said their citizens should leave Lebanon.
A senior security source in Lebanon told Reuters that 14,000 people had left the country on Thursday alone, mostly Europeans.
* With additional reporting from Reuters