Lokomotiv Moscow midfielder Dmitri Tarasov revealed the picture of Putin following his side's 2-0 defeat by Fenerbahce, with the Russian President depicted in a navy cap above the words: "The most polite President."
"Polite people" was an expression used in Russia to describe the troops in unmarked uniforms who took control of Crimea during its annexation from Ukraine.
After Turkey shot down a Russian warplane near the Turkish-Syrian border in November tensions have been high between the two nations. The Europa League round-of-32 first leg was the biggest sporting encounter involving teams of the two countries since relations had deteriorated.
UEFA confirmed to CNN that disciplinary proceedings have been opened following Tuesday's game, with both Lokomotiv and Fenerbahce having been charged by European football's governing body.
The Russian side has been charged with "improper conduct of Lokomotiv player Dmitry Tarasov after the match," with UEFA rules stating that "players must not reveal undergarments that show political, religious, personal slogans, statements or images, or advertising other than the manufacturer logo."
Fenerbahce, meanwhile, has been charged with having had "stairways blocked" in its Sukru Saracoglu Stadium.
Tarasov said he chose to wear the Putin T-shirt to show his "support" for the Russian President.
"It's my president. I respect him and decided to show that I'm always with him and prepared to give my support," Tarasov is widely reported as telling Russian news agency R-Sport
"What was written on that shirt was everything that I wanted to say."
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However,Tarasov's action was labelled "a Putin provocation" by the Turkish media.
Despite Turkish-Russian tensions, UEFA has refused to separate the two nations in draws for the Europa League and Champions League, as well as for this summer's Euro 2016, though last season Europe's governing body kept Russian and Ukrainian clubs apart in European competition due to the political problems between the two neighbors.
Fenerbahce won Tuesday's clash thanks to two goals from Josef Souza.