Besiktas coach Slaven Bilic was also banned by the Turkish Football Federation for three games and Galatasaray's Brazilian midfielder Felipe Melo was handed a two-game suspension after he received a red card.
Police used teargas in an attempt to restrain fans who rushed on to the field after Melo was sent off.
Galatasaray were leading 2-1 in the third minute of stoppage-time when the match was halted, sending the players sprinting for the safety of the dressing-rooms.
The match was the first Istanbul derby of the season and followed months of civil unrest in Turkey's largest city over government plans to demolish a park at the central square of Taksim.
Besiktas's politicised fan base, dubbed "Carsi", was a prominent force in the anti-government protests and often clashed with police during the peak of the unrest in June.
At Sunday's match, Besiktas fans chanted; "Everywhere is Taksim, everywhere is resistance," a popular chant from the park protest.