"Syria is the most notable absentee at our conference, and we feel the weight of its absence," Gibran Bassil said.
"Syria should be among us... without us having to wait for a permission for it to return," he added at a meeting with other ministers from Arab League nations.
The Arab League suspended Syria in November 2011 when the death toll rose in the regime's brutal repression of anti-government protests.
But in recent years, Bashar al-Assad's forces have gained the military upper hand against rebels and jihadists, and efforts to bring his government back into the Arab fold appear underway.
In December, Sudan's President Omar al-Bashir made the first visit by any Arab leader to the Syrian capital since 2011, and the United Arab Emirates reopened its embassy in Damascus after closing it in 2012.
On Thursday, the head of the Arab League, Ahmed Abul Gheit, said member states have not reached a consensus on Syria's return to the 22-member bloc.
"When there is an Arab consensus, and when we are sure there is no objection from one side or the other, it will be as simple as putting it on the agenda of a meeting" of Arab foreign ministers, he said.
Syria's war has killed more than 360,000 people and displaced millions since it started with anti-government protests.
Only the presidents of Somalia and Mauritania are expected to attend the Arab Economic Summit on Sunday.
Lebanese newspapers ran despairing headlines on Friday.
"The Beirut shock... a summit without heads of state," the country's oldest Arabic-language newspaper An-Nahar said.
The conference is set to discuss the digital economy, as well as a long-suggested project for an Arab free trade zone.
Lebanon also hopes to put forward an initiative calling on countries in the region to help spread the burden of 1.5 million refugees living on its soil.
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