The Belgian, who enjoyed an auspicious Premier League debut against Crystal Palace on Saturday, was not included in the club's five-man B list for the competition and was absent from training.
Januzaj, 18, will instead face Bayer's under-19 side in the Uefa Youth League, though he can be named in future Champions League squads with 24 hours notice because of his age.
His exclusion is odd considering 20-year-old Will Keane, still recovering from a knee ligament injury which has sidelined him for over a year, is included on the B list.
Shinji Kagawa resumed training after a bout of flu last week while Phil Jones and Darren Fletcher trained away from the group. Danny Welbeck, who missed the Palace win, was not involved.
Moyes had a brief taste of the Champions League when Everton lost their 2005 play-off to Manuel Pellegrini's Villarreal 3-2 on aggregate. The Scot will face Pellegrini this weekend in the season's first Manchester derby at Eastlands.