A junior cabinet minister will lead the Egyptian delegation instead.
Saudi Arabia had said it would only send its Arab League representative rather than King Abdullah, and Lebanon is boycotting the summit completely.
The political situation in Lebanon, which has prompted disputes between Arab countries, is being blamed for the upheaval, correspondents say.
Lebanon has been without a president since November because of disputes between the pro-Western government, supported by Saudi Arabia and Egypt, and the opposition, which is supported by Syria and Iran.
Each side blames the other for blocking a final deal.
And Syria's detractors have used that as an issue with which to embarrass it as it hosts the Arab summit, says BBC regional analyst Andrew Bolton.
Syria was a dominant player in Lebanon for decades before it was made to withdraw its troops in 2005 in the aftermath of the killing of former Lebanese Prime Minister Rafik Hariri - an act which Damascus says it had nothing to do with.
Syria does not want what it sees as its remaining influence in Lebanon diminished for the relatively short-term gain of a full house of heads of state at the Arab summit, our correspondent says.
Jordan has not yet said whether it will be sending a representative to the summit.
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