Lokomotiv Moscow midfielder Dmitri Tarasov's vest showed Mr Putin in a navy cap along with the words "the most polite president".
The politically-charged Europa League match was the biggest sporting encounter between the nations since Turkey shot down a Russian jet in November.
Turkish side Fenerbahce won 2-0.
Lokomotiv Moscow are now likely to face punishment because European football's governing body Uefa does not allow political statements during matches.
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But Tarasov later defended his behaviour.
"It's my president. I respect him and decided to show that I'm always with him and prepared to give my support," he told Russian news agency R-Sport.
"What was written on that shirt was everything that I wanted to say," he added.
Turkish newspaper Yeni Safak described the gesture as "a Putin provocation".
Relations have been tense since Turkey downed a Russian fighter that it said was in its airspace.
The incident sparked a continuing war of words between Mr Putin and Turkish President Recep Tayyip Erdogan over the conflict in Syria.
Before the match in Istanbul, bottles were thrown at the Lokomotiv team bus as it made its way to the stadium. Turkish police said they made three arrests.
However, Uefa rejected calls to separate Russian and Turkish clubs in European competitions and will also not separate the two nations in the draw for this summer's European Championship.
A Russian footballer taunted Turkish fans by pulling off his shirt to reveal a picture of President Putin after a match in Istanbul.