The Palestinians presided over the council's latest session earlier this month and had been due to stay in the role until March.
The Palestinians have stepped down from a key Arab League role in protest at the regional bloc's failure to take a stand against Israeli-Arab deals.
Palestinian foreign minister Riyad al Maliki on Tuesday announced the decision to resign from the rotating presidency of the Council of the Arab League, after its failure to agree a draft resolution condemning a normalisation accord between the UAE and Israel.
"The state of Palestine ... refuses to record in its history the association of its presidency with the regression in values and principles that was evident in the last meeting of the council of foreign ministers," Maliki said in the West Bank town of Ramallah.
The Palestinian delegation had tabled a draft resolution at the meeting of the council, which brings together foreign ministers of the 22-member bloc, to condemn the normalisation accord.
The Cairo meeting came ahead of another such deal being announced by Bahrain with the Jewish state. Both deals were signed in Washington on September 15.
The Gulf agreements broke with years of Arab League policy on the Israeli-Palestinian conflict and were condemned by the Palestinians as a "betrayal".
Arab plan pushed aside
In 2002, the bloc adopted a Saudi-proposed peace plan which was renewed as recently as 2017.
It offered normalisation only in return for a full Israeli withdrawal from territories it occupied in the 1967 Six-Day War, a Palestinian state with east Jerusalem as its capital and a just solution for Palestinian refugees.
The Arab plan has been pushed aside by the US administration, which after several delays unveiled a controversial peace blueprint of its own in January.
It promised Washington's blessing for Israel's eventual annexation of swathes of the occupied West Bank.
The United Arab Emirates government hailed a clause in its US-brokered deal that appeared to put any Israeli annexations on hold.
But Israel retorted that any delay would be short-lived and its annexation plans remained on the table.