Citing Turkish diplomatic sources, the state-run Anatolia news agency said Turkey has also temporarily recalled its ambassador to the Syrian capital. Sources said Ambassador Ömer Önhon and Turkish diplomatic staff in Damascus are expected to arrive in Ankara soon.
A ministry official, speaking to the Associated Press on condition of anonymity in line with ministry regulations said Monday the embassy was being closed due to the security situation in Syria.
Prime Minister Recep Tayyip Erdoğan has recently said that Turkey was on a brink of breaking diplomatic ties with Syria and withdrawing its ambassador.
Last year Erdoğan told Syrian President Bashar al-Assad he should quit, having lost patience with his former friend's refusal to end a violent crackdown on popular unrest over the past year.
Turkey is providing sanctuary to more than 16,000 Syrians who have fled the violence in their homeland, has given shelter to soldiers from the rebel Free Syrian Army, and allows the Syrian opposition to meet regularly in İstanbul.
On April 1, Turkey will hold a meeting of "Friends of Syria", grouping mostly Arab and Western governments, to find ways to pressure Assad into halting his military clampdown, during which the country has drifted towards civil war.
Many of those governments closed their embassies in Damascus earlier this month.
The meeting of foreign ministers will be held in Istanbul, where leading Syrian dissidents were gathering on Monday and Tuesday in an attempt to bridge divisions within the opposition and instil confidence in the Syrian National Council umbrella organisation.
More than 50 countries were represented at the first meeting of the "Friends of Syria" group in Tunis in late February.
Last week the foreign ministry called on all Turkish citizens in neighbouring Syria to return to Turkey as soon as possible, saying it planned to close the consular section of its Damascus embassy, which it did on March 22.
All embassy staff have been withdrawn, including the ambassador, who had recently returned to Damascus, having earlier been brought back to Ankara for many months as relations with Assad's government turned icy.
Turkey, a Muslim member of NATO, has the second largest army in the Western alliance and has gathered increasing clout in the Middle East by siding with people rather than rulers during the uprisings that have shaken the Arab world since late 2010.
Turkish diplomats' families were brought home last year after an attack on the embassy by demonstrators who were angry that Turkey had taken sides against Assad.