MENA says the decision came during the league foreign ministers' meeting today.
The move aligns the 22-member league firmly behind Saudi Arabia and the Saudi-led bloc of six Gulf Arab nations, which made the same move against Hezbollah earlier this month.
However, the Saudi ambassador in Cairo, Ahmed Qattan, told the satellite TV station Al Arabiya that the vote was not unanimous as Lebanon and Iraq abstained.
The Arab League move, as the GCC one earlier, ramps up the pressure on Hezbollah, which is fighting on the side of President Bashar Assad in Syria. It comes less than two weeks after Saudi Arabia cut $4 billion in aid to Lebanese security forces.