A UEFA statement on Thursday said the probe had been ordered following the "alleged misbehaviour" of Fenerbahce supporters.
Dynamo won 2-1 on the night, after extra-time, to go through by the same score on aggregate to the third qualifying round against Austria's Sturm Graz.
In the 57th minute, shortly after Fenerbahce midfielder Ismail Yuksek was sent off, Vitaliy Buyalskyi put the Ukrainian side ahead.
His celebration was met with chants of 'Vladimir Putin' by many Fenerbahce fans.
"I didn't expect such chants - they were deplorable," Dynamo coach Mircea Lucescu told Turkish newspaper Fanatik after skipping Wednesday's post-match news conference in protest at the chants.
Though Fenerbahce missed a penalty Attila Szalai levelled to force extra-time but Oleksandr Karavaev scored a 114th-minute winner to put Kiev through.
The victory was remarkable given Dynamo have only been playing friendly games across Europe since Russia invaded Ukraine in February and the nation's football league was suspended.
Dynamo played last week's "home" leg in Lodz in Poland.
Vasyl Bodnar, Ukrainian Ambassador to Ankara, said on Twitter he was saddened by the chants but thanked those who stood against the "inappropriate actions" of the fans.
Bodnar added that it was "very saddening" to hear the reaction of the Fenerbahce fans at a time when civilians in Ukraine were dying in Russian attacks on the country.
In a statement on Thursday, Fenerbahce said the chants made by "some" fans did not represent the club, its position, or its views, adding that it stood firmly against the war in Ukraine.
Fenerbahce said the chants lasted 20 seconds and were prompted by the "exaggerated" celebrations of some Kyiv players after the goal.
"Whatever the reason may be, we as the Fenerbahce Sport Club absolutely reject the reaction coming from parts of our stands," the club said, adding it was unfair to put blame on all its fans or the club for an act that "never represents our values."
NATO member Turkey shares a maritime border with Ukraine and Russia in the Black Sea and has good ties with both.
