The Red Devils left-back suffered a broken leg in Tuesday night's 2-1 Champions League group stage loss to Dutch champions PSV Eindhoven in Holland.
Januzaj, who is on a season-long loan with Borussia Dortmund, saw the incident which is likely to see Shaw sidelined for a lengthy spell.
The Belgian Tweeted:
Horrible to see what happened I wish u all the best my brother and stay strong you will comeback even stronger @LukeShaw23
— Adnan Januzaj (@adnanjanuzaj) September 15, 2015