The decision to send the relatively low-ranking diplomat reflects the strained ties between Riyadh and Damascus.
Emile Lahoud's term as Lebanese president ended in November. Since then, 17 attempts to vote in a replacement have been postponed due to deadlock between the ruling coalition and the opposition over the make-up of the government.
The latest attempt to convene parliament for the vote was scheduled to take place on Tuesday, but late on Monday the session was postponed until April 22.
Damascus, along with Tehran, supports the Hezbollah-led Lebanese opposition, while Cairo and Riyadh back the ruling March 14 coalition, led by Fouad Siniora, the prime minister.
It is unclear whether Lebanon will boycott the summit, but Beirut's delegation did not attend Monday's preparatory meeting ahead of the conference.
Nabih Berri, the Lebanese parliamentary speaker and opposition leader, said late on Sunday that he would call on rival politicians to engage in dialogue if no solution was reached during the summit.
"If no solution is found to the Lebanese crisis after the Arab summit, I will hold consultations with Arab countries such as Egypt, Syria and Saudi Arabia ... in order to convene dialogue meetings," he said.
"The agenda of these meetings will centre on the formation of a national unity government and a new electoral law."
Berri said that he would issue invitations for meetings to be held in May, adding that he hoped that "all the parties will respond to this call".
Lebanon's feuding politicians held a series of national dialogue talks in 2006, but failed to reach agreement over the disarmament of Hezbollah.