Play twice had to be stopped in the Group D clash as flares and firecrackers were thrown onto the pitch at Signal Iduna Park, during a match that saw the Bundesliga side run out 4-1 winners.
Galatasaray have already been involved in off-field incidents this season in the competition, and were charged following similar scenes in their meeting with Arsenal last month.
UEFA have now opened disciplinary proceedings against the Turkish club and Dortmund, with the latter charged with throwing objects and insufficient organisation.
Galatasaray have been charged with crowd disturbances, field invasions by supporters and the setting off/throwing of fireworks and missiles.
The charges are due to be settled by UEFA's Control, Ethics and Disciplinary Body next Thursday.
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