Arabi, 80, took over as League chief from fellow Egyptian diplomat Amr Moussa in 2011.
He had served as foreign minister in the Egyptian government that came to power after the ouster of longtime president Hosni Mubarak earlier that year.
Signup to our newsletter and follow us on Facebook and Twitter!
"I have asked the Egyptian government not to think about renewing my mandate," Arabi told reporters at the League's headquarters in Cairo, adding that his present tenure would end in early July.
Traditionally, the secretary general of Arab League has held the post for two terms, and Cairo has always insisted that it be held by an Egyptian diplomat.
Since becoming secretary general, Arabi has had to manage a number of sensitive issues, including the conflicts in Syria, Iraq and Libya, as well as the rise of the Islamic State jihadist group.