Cairo also wants the League's members to hand over wanted Islamists linked to the Brotherhood to which deposed president Mohamed Morsi belongs.
Egypt's military-installed government listed the Brotherhood as a terrorist group last week, after officials accused the movement of a suicide bombing that killed 15 people in a police station on Tuesday.
The Brotherhood, the largest Islamist movement in the region, has a presence in most Arab countries. It condemned the bombing, which was claimed by Al-Qaeda-inspired militants based in the restive Sinai peninsula.
The treaty coordinates anti-terrorism measures between signatories.
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"The signatories are responsible for implementing the treaty," Abdelatty told AFP, adding the members would have to stop financing the group and hand over Brotherhood fugitives to Egypt.
An Arab League official said 18 of the Arab League's 22 members had ratified the treaty.
The Arab League said it has notified its members of Egypt's designation of the Muslim Brotherhood as a terrorist group.
Morsi and dozens of Brotherhood leaders face trials on various charges, including colluding with militants to carry out attacks in Egypt.
The movement had won every election in Egypt after the 2011 overthrow of strongman Hosni Mubarak.
It successfully fielded Morsi in the country's first free presidential election in 2012, but he lasted only a year in power before the military toppled him amid massive street protests demanding his resignation.
Since then more than 1,000 people, most of them Islamists, have been killed and thousands imprisoned in a crackdown on his supporters.