The announcement is further indication of the complexities of implementing the truce, which the government and opposition approved this week.
According to the agreement announced by the US and Russia, the truce does not apply to jihadists from the Islamic State group or Al-Qaeda's affiliate Al-Nusra Front.
Al-Nusra militants make up one-fifth of rebel fighters in Daraya.
"The Syrian army is committed to the decision of the Syrian leadership when it comes to the ceasefire, which will not include areas where Al-Nusra Front and Daesh are fighting," an army general said, using the Arabic acronym for IS.
"Therefore, Daraya is not included in the cessation of hostilities agreement, because Al-Nusra Front is one of the factions inside the town," he added during a patrol inside Daraya.
Signup to our newsletter and follow us on Facebook and Twitter!
The general said he estimated between 1,000 to 2,000 anti-government combattants remained in the town.
Daraya is the largest rebel bastion west of Damascus where fighting is still taking place, said Rami Abdel Rahman, head of the Syrian Observatory for Human Rights monitoring group.
"It's an essential opposition stronghold that has been out of regime control for nearly four years," Abdel Rahman said.
According to the agreement announced Monday, a task force headed by the United States and Russia is responsible for delineating territories held by IS and Al-Qaeda that would be excluded from the agreement.
Analysts say that given the facts on the ground -- in particular the complicated make-up of Syria's opposition forces and frequently shifting frontlines -- the ceasefire may be doomed to fail.
While IS control over territory is relatively clear and stable, Al-Nusra works closely with many other rebels groups, particularly in the north.
More than 270,000 people have been killed since Syria's war erupted in March 2011, and millions have fled their homes.