The Polish side emerged as 6-1 victors from their two-legged third qualifying round clash, and the investigation relates to the involvement of attacker Bartosz Bereszynski.
The 22-year-old came on as an 86th-minute substitute in Wednesday's second leg, at which point Celtic required six goals to reach the play-off round.
"The club announces that, in connection with the Champions League third qualifying round second-leg match Celtic FC - Legia Warsaw, UEFA has opened an investigation into the participation of Bartosz Bereszynski," it read.
"The club has prepared relevant information and explanations which will be sent to UEFA today. The result of the investigation will be announced immediately after its completion."
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