The Polish side emerged as 6-1 aggregate victors from their two-legged third-qualifying-round clash but face scrutiny for 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, but was sent off in Legia's final Europa League tie last season against Apollon Limassol and received a three-match ban.
Uefa is now set to determine whether the player should have been suspended for Wednesday's game, with Legia announcing the news in a statement on their website on Thursday.
"The club announces that, in connection with the Champions League third qualifying round second-leg match [against Celtic], 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."
The news could give hope to Ronny Deila's men of a reprieve after the Champions League, the club's most lucrative competition and a source of excitement under previous boss Neil Lennon, looked to have slipped through their fingers.