The Russian side have been charged over the improper conduct of their supporters in Slovakia, whose actions brought about a 20-minute delay early in proceedings.
Dutch referee Kevin Blom led both sets of players off the field after flares were thrown on to the pitch by the travelling faithful. The visiting team re-emerged to plead with their own fans for calm, only to be met by a fresh barrage, before the game eventually resumed. Spartak went on to win 2-1.
Zilina face a charge of insufficient organisation relating to the same incident, along with a separate count of improper conduct by the team after their players received five yellow cards during the game.
Both cases will be heard at Thursday's meeting of the UEFA control and disciplinary body.
