Clashes between groups thought to consist of supporters of the two clubs erupted in the university district of the city before the match, with Barcelona running out 6-0 winners in a dress rehearsal for May's Copa del Rey final.
Following the game, Barcelona and Alaves commented on the incidents.
"FC Barcelona laments and condemns the incidents that occurred this afternoon in the city of Vitoria before the game against Deportivo Alaves," read a statement from the Catalans.
"The club reiterates its utter rejection of any violent conduct and trusts that the competent authorities will be able to verify the source and responsibility of these events as soon as possible."
Alaves confirmed the club will cooperate with local police to find the perpetrators of the disruption.
The statement from Alaves read: "Alaves strongly condemns the violent events that took place on the morning of February 11 in the area of the universities between alleged supporters of Alaves and Barcelona.
"The club is available to the authorities and, if the persons involved are found to be supporters, Alaves will assess the measures to be used with respect to these people."
The match itself was marred by a horror injury to Barcelona's Aleix Vidal, while Lionel Messi, Neymar and Luis Suarez were all on the scoresheet.