Fenerbahce players were met with violence as they celebrated their 3-2 victory at Papara Park in Trabzon.
Fenerbahce's Bright Osayi-Samuel and Michy Batshuayi both tried to intervene as security services entered the field.
"It is never acceptable for violence to take place on football pitches - above all, sport is gentlemanship," Turkey's Interior Minister Ali Yerlikaya said.
"An investigation has been initiated immediately to identify the spectators who entered the pitch and to investigate the incidents that took place at the end of the match," he wrote on X, formerly known as Twitter.
Fifa president Gianni Infantino said the incidents were "absolutely unacceptable".
"I have said it before, and I will say it again - without exception, in football, all players have to be safe and secure to play the game which brings such joy to so many people all over the world," he said.
"I call on the relevant authorities to ensure that this is respected at all levels and for the perpetrators of the shocking events in Trabzon to be held accountable for their actions."
Tensions started to rise in the 87th minute when objects were thrown on to the field after Batshuayi scored what proved to be the winner for the visitors.
