Manager Brendan Rodgers submitted his selections to UEFA on Wednesday (AEST), with Arzani failing to make the cut alongside Scott Allan and Marvin Compper.
The 19-year-old's omission comes as a surprise after arriving on a two-year loan deal from Manchester City, having been tipped to prosper under Rodgers' stewardship.
Arzani will instead have to wait to make his European bow as the Hoops prepare to face RB Leipzig, Red Bull Salzburg and Socceroo Alex Gersbach's Rosenborg in Group B.
Meanwhile, fellow Australia midfielder Tom Rogic earned his place in the squad and will be integral to Celtic's continental success this season.
Rogic was instrumental this past weekend, creating the game's only goal as Celtic ran out deserved winners over Old Firm rivals Rangers at Parkhead.
Celtic kick off their Europa League campaign at home to Rosenborg on September 21.
Celtic's Europa League squad
Goalkeepers: Craig Gordon, Scott Bain, Conor Hazard*, Ryan Mullen*
Defenders: Kieran Tierney*, Emilio Izaguirre, Kristoffer Ajer, Jack Hendry, Jozo Simunovic, Cristian Gamboa, Dedryck Boyata, Mikael Lustig, Filip Benkovic, Anthony Ralston*, Daniel Church*, Wallace Duffy*, Kerr McInroy*, Stephen Welsh*, Lewis Bell*
Midfielders: Scott Brown, Scott Sinclair, Lewis Morgan, Tom Rogic, Olivier Ntcham, Youssouf Mulumbu, Callum McGregor, James Forrest, Eboue Kouassi, Ewan Henderson*, Scott Robertson*, Paul Kennedy*, Ross McLaughlin*, David Mckay*, Kristi Marku*, Mark Hill*, Kieran Mcgrath*, Regan Hendry*
Forwards: Leigh Griffiths, Jonny Hayes, Ryan Christie, Odsonne Edouard, Michael Johnston*, Grant Savoury*
*Indicates player list B
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