The US State Department has urged Americans to "carefully consider" the threats when traveling to Saudi Arabia.
Saudi Arabia has been leading a coalition at war in Yemen since March 2015, when the oil-rich kingdom intervened to push back Houthi rebels and reinstate the government of President Abd-Rabbu Mansour Hadi.
Iran, Lebanon reject Arab League criticism as tensions mount
The groups described the statement of Arab League foreign ministers following their emergency meeting in Cairo as unsafe and said Hezbollah is the most significant force standing against the Zionist regime's aggression and terrorism, a Farsi report by IRNA said. "We want to hold countries where Hezbollah is a partner in government responsible, specifically Lebanon".
It also says terrorist attacks "can occur without warning anywhere" in Saudi Arabia.
Arab League chief Ahmed Aboul-Gheit, who visited Lebanon and met with Parliament Speaker Nabih Berri on Monday, said Lebanon "cannot be an arena for any Arab-Iranian confrontation".
The source highlighted that the people of the Arab world, having been a witness to the conspiracy of the so-called "Arab Spring", know very well what Hezbollah and Iran have done in the course of confronting the Takfiri terrorism and know the sacrifices they have made to foil this conspiracy and resist the Zionist expansionist aggression.
The warning comes two weeks after US-allied Saudi Arabia said it had shot down a ballistic missile fired by Iran-backed Houthis from Yemen towards the Saudi capital Riyadh.
The comments came during increasing tension between Saudi Arabia and Lebanon, after the unprecedented resignation of Lebanese Prime Minister Saad al-Hariri from Riyadh. Saudi Minister for Gulf Affairs Thamar Sabah has warned the Lebanese they must choose "either peace, or to live within the political fold of Hezbollah".
Sunni Saudi Arabia and Shiite Iran have long vied for regional supremacy, and support rival proxies across the Middle East.