The Poles won 2-0 in the Capital to beat Ronnie Deila's side 6-1 on aggregate and book their place in the play-off round.
Defeat for the Hoops should have meant they dropped into the final qualifying round for the Europa League but they could now be reinstated to Europe's premier club competition.
Legia right-back Bartosz Bereszyńskiego was red carded last season but wasn't registered in the squad which beat St Patrick's to set up the tie with Celtic in the third qualifying round.
He appeared for the final four minutes of the match at Murrayfield as Henning Berg's side eased to victory.
And Uefa are now set to launch a probe into the matter to determine if the Poles can keep their place in the play-off round, which will be drawn alongside the Europa League on Friday.
A Legia statement said: "[The] Club announces that in connection with the second leg, third qualifying round of the Champions League Celtic FC - Legia Warsaw, Uefa opened an investigation on the participation by Bartosz Bereszyńskiego.
"Club prepares relevant information and explanations which will be sent to Uefa today.
"The result of the investigation will inform immediately after its completion."