All 176 people on board died when the Ukrainian International Airlines plane went down near Tehran on Wednesday, shortly after Iran launched missiles at US forces in Iraq over the killing of a top Iranian general.
American, British and Canadian officials say intelligence sources indicate Iran shot down the plane, perhaps unintentionally, but this has been denied by Tehran.
Several airlines had already announced they would avoid Iranian and Iraqi airspace as tensions in the region soared.
A Lufthansa flight between Frankfurt and Tehran on Thursday turned back an hour after takeoff because of security concerns.
Austrian Airlines meanwhile said late Thursday that its flight to Tehran that day was ordered to return to Vienna after a stopover in Sofia.