"A 'regime of silence' has been introduced from 00:01 on March 6 to 23:59 on March 20 (Damascus time) in the area of Eastern Ghouta," the ministry said in a statement on Tuesday.
It added that "no violations" had so far been reported.
The Army of Islam (Jaish al-Islam), a powerful rebel faction, is headquartered in Eastern Ghouta, the last opposition stronghold near Damascus.
The district has faced a blistering army offensive in recent months and is near opposition-controlled areas of Damascus increasingly targeted by the government.
Syria's Al-Watan daily, which is close to the government, on Tuesday quoted a "source close to the state's efforts to conclude national reconciliation in flashpoint areas" as saying he did not have "any information" on a new agreement in the eastern neighbourhood of Damascus and Eastern Ghouta.
The Syrian Observatory For Human Rights, a Britain-based monitor of the conflict, reported Tuesday that raids hit many towns in the Eastern Ghouta district as well as rebel districts in eastern Damascus.
Syria's conflict has killed more than 310,000 people since 2011. Russia began a bombing campaign in support of Syrian President Bashar al-Assad in September 2015.
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