Bahrain and the United Arab Emirates supported the Saudi request, which was also approved by Djibouti, the current chair of the pan-Arab bloc, said the document shown to AFP by diplomats on Sunday.
According to the memo, the Saudi request was based on a missile the Sunni-ruled kingdom says its air defences intercepted near Riyadh after being fired from Yemen on November 4.
A Saudi-led coalition has been battling Shiite Huthi rebels in Yemen, and it has accused the Iran-backed rebels of firing the missile.
Saudi Arabia´s powerful Crown Prince Mohammed bin Salman later accused Iran of "direct military aggression" against the kingdom by supplying the rebels with ballistic missiles.
But Iran denied any involvement in the missile attack, with President Hassan Rouhani warning that the Islamic republic´s "might" would fend off any challenge.
According to the memo, Saudi Arabia decried what it described as "sabotage" and "terrorism" over a pipeline fire in Bahrain on Friday that temporarily halted oil supplies from its territory.
Tehran also rejected any involvement in the incident, calling the allegation "childish".
In its request for the meeting of Arab foreign ministers, Saudi Arabia referred to those two incidents "in addition to the violations committed by Iran in the Arab region, which undermines security and peace, not only in the Arab region, but around the globe," according to the memo.
Saudi Arabia has been at the forefront of a dispute with Qatar since June 5, leading a group of nations including Bahrain, Egypt and the UAE in accusing Doha of supporting terrorism.
Riyadh has for its part been accused of being behind last weekend´s resignation of Lebanese prime minister Saad Hariri, in a televised address from Riyadh.
The Arab League has 22 members, but Syria´s membership was suspended at the end of 2011 following months of brutal repression of anti-government demonstrations and an opposition movement supported by Gulf monarchies.