In a televised address, Prime Minister Edi Rama said it was "impossible for Albania to take part in this operation."
The announcement was greeted by a loud cheer from some 2,000 protesters camped outside Rama's office who opposed the plan to dismantle the weapons in Albania.
The Organisation for the Prohibition of Chemical Weapons has been discussing a plan to destroy Syria's estimated 1,000-metric ton arsenal, which includes mustard gas and the deadly nerve agent sarin.
Meanwhile, outside Rama's office, hundreds of youths camped overnight to protest the plan.
"We don't have the infrastructure here to deal with the chemical weapons. We can't deal with our own stuff, let alone Syrian weapons," said 19-year-old architecture student Maria Pesha, echoing the fears of many residents. "We have no duty to obey anyone on this, NATO or the US.