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.
Wayne Rooney trained without his headband
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.