A family stands neart a billboard showing Russian President Vladimir Putin and Syrian President Bashar Assad in Damascus, Syria, March 7, 2022. AP
The announcement marks one of the strongest responses to date by Turkey, which has cultivated close ties with Moscow despite being a member of the NATO defence alliance, to Russia's two-month military assault on Ukraine.
"We closed the airspace to Russia's military planes -- and even civilian ones -- flying to Syria. They had until April, and we asked in March," Turkish media quoted Cavusoglu as saying.
Cavusoglu said he conveyed the decision to his Russian counterpart Sergei Lavrov, who then relayed it to President Vladimir Putin.
"One or two days later, they said: Putin has issued an order, we will not fly anymore," Cavusoglu was quoted as telling Turkish reporters aboard his plane to Uruguay.
Cavusoglu added that the ban would stay in place for three months.
There was no immediate response to Turkey's announcement from Russia, which together with Iran has been a crucial supporter of Syrian President Bashar al-Assad during the war-torn country's civil war.
Turkey has backed Syrian rebels during the conflict.
Ankara's relations with Moscow briefly imploded after Turkey shot down a Russian warplane near the Turkish-Syrian border in 2015.
But they had been improving until Russia's invasion of Ukraine, which Turkey views as an important trade partner and diplomatic ally.
Turkey has been trying to mediate an end to the conflict, hosting meetings between Russian and Ukrainian negotiators in Istanbul, and another between Lavrov and Ukrainian counterpart Dmytro Kuleba in Antalya.
Ankara is now trying to arrange an Istanbul summit between Putin and Ukrainian President Volodymyr Zelensky, although Cavusoglu conceded that the prospects of such talks at this point remain dim.
"If they want a deal, it's inevitable," Cavusoglu was quoted as saying. "It might not happen for a long time, but it can happen suddenly."