Shehab will attend the Damascus summit, due to begin on Saturday, in place of Egypt's president.
The snub reflects tensions with Syria over the political crisis in Lebanon, the continuation of which Egypt and other powers blame on Syria.
Snub
The move comes after Saudi Arabia said it would only be sending its Arab League ambassador to the summit and Lebanon announced it would be boycotting the meeting altogether.
Relations between Syria and the Arab allies of the US have deteriorated over a string of issues, including Syria's support for the Palestinian group Hamas and its alliance with Iran, as well as the situation in Lebanon.
"This announcement by Egypt was really rather unexpected," said Amani Soliman, Al Jazeera's Middle East editor.
"It seems that Saudi Arabia really set the tone."
Walid al-Moallem, Syria's foreign minister stopped short of criticising Saudi Arabia and Egypt on Wednesday, but suggested the US was behind the Lebanon's boycott.
Political stalemate
Egypt and Saudi Arabia have both accused Damascus of preventing Lebanon from electing a new president.
Lebanon's presidency has been vacant since November, when the term of Emile Lahoud, the pro-Syria president, ended.
The Lebanese opposition, led by Hezbollah, which has links to Syria, has been boycotting parliament to prevent the body from choosing a successor.
The US and its Arab allies, on the other hand, have heavily backed Lebanon's government, led by Fouad Siniora, the prime minister.