"The Embassy of France in Ankara, as well as the Consulate General in Istanbul will be closed from Wednesday July 13, 1:00 pm (1000 GMT), until further notice," the embassy said in a statement.
It did not give any further details on how the closure would be implemented.
The move came shortly after Paris said it had cancelled its planned traditional July 14 events at diplomatic missions in Turkey for security reasons after receiving intelligence of a "serious" threat.
France's consulate in Istanbul, its embassy in Ankara and its mission in the Aegean city of Izmir were all to have held celebrations marking the July 14 Bastille Day.
French consul to Istanbul Muriel Domenach wrote on Twitter the events in all three cities had been cancelled "for security reasons" and France was in touch with the Turkish authorities.
Earlier, the Istanbul consulate had sent an email message to French citizens in Turkey saying that there had been "concurring information of a serious threat against the organisation of the July 14 celebrations in Turkey."
It said the decision had been taken in coordination with the Turkish authorities.
Turkey is on a high security alert following the June 28 attack on Istanbul's main airport which was blamed on Islamic State (IS) jihadists and killed 47 people.
Thirty-seven suspects have been placed under arrest over suspicion of involvement in the attacks. Of these, 15 are Turks and 22 foreigners, according to official media.
Authorities have said a number of citizens of ex-Soviet republics are among the suspects, raising concerns over the threat to Turkey from Islamist militancy in the Central Asia and the Northern Caucasus.
But of seven suspects arrested earlier this week, three are Algerian, two Tunisian and two Egyptian, the state-run Anadolu Agency said.
The bombing at Ataturk International Airport in Istanbul followed a spate of attacks across the country this year blamed on IS jihadists and Kurdish militants.
Several foreign missions in Turkey, including the embassies and consulates of Germany and the United States, have closed for short periods this year due to a security threat.