Having made 18 Bundesliga appearances during his first season with the club, Burkina Faso international Bance was sent to Fortuna Dusseldorf on loan last term.
Bance, who was contracted until 2015, scored just two goals in 16 outings in the second tier and has now been deemed surplus to requirements at Augsburg.
"We wish Aristide Bance all the best for his future," read a short statement.
Meanwhile, attacker Fetsch has been loaned out to Dynamo Dresden for the duration of the season.
Fetsch spent most of last season on loan at Energie Cottbus, but did manage one top-flight appearance before his departure.