Calderwood confirmed Kyle had been given permission on Tuesday to join the Russian club's pre-season training camp in Turkey, but revealed he had received a phonecall from the Scotland international to say he was not going.
The Killie boss then found out through the media the 28-year-old had flown out on Wednesday before playing in a trial match yesterday.
Kyle was due to arrive back in Scotland on Friday evening and may be left out of the squad for Saturday's Clydesdale Bank Premier League game at Hibernian.
A nonplussed Calderwood said: "We gave him permission to go on Tuesday and that got called off.
"The next thing we hear, he went on Wednesday.
"We'll have a look and see, have a talk to him and see exactly what's happened and take it from there."