The Blues spent in excess of £300 million in the January transfer window on eight new signings.
However, UEFA rules allow only three new players to be registered for the knockout stages.
Enzo Fernandez, whose £107 million move from Benfica set a new British transfer record, has been included alongside Mykhailo Mudryk and loan signing Joao Felix.
That meant there was also no place for Aubameyang.
The former Arsenal captain had become a peripheral figure under Graham Potter even before the wave of new arrivals in January.
By contrast, Badiashile has made an impressive start to his Chelsea career since joining from Monaco.
The centre-back has been part of a defence that kept back-to-back clean sheets against Crystal Palace and Liverpool in his two appearances to date.
Chelsea face Borussia Dortmund in the last 16 of the Champions League.
The Germans will host the first leg on February 15 with the return at Stamford Bridge on March 7.
