East Java Governor Khofifah Indar Parawansa said the provincial government will give 10 million rupiah ($650) in compensation to the families of the victims and the local regency will give five million rupiah.
"This is part of our empathy to the families of the victims," she said.
Fan violence is an enduring problem in Indonesia, where deep rivalries have previously turned into deadly confrontations.
Arema FC and Persebaya Surabaya are longtime rivals.
Persebaya Surabaya fans were not allowed to buy tickets for the game due to fears of violence.
However Indonesia's coordinating minister for political, legal and security affairs, Mahfud MD, said organizers ignored the recommendation of authorities to hold the match in the afternoon instead of the evening.
And he said the government had recommended only 38,000 tickets be printed, but there was instead a sell-out crowd of 42,000.
"The government has made improvements to the implementation of football matches... and will continue to improve. But this sport, which is a favorite of the wider community, often provokes supporters to express emotions suddenly," he said in an Instagram post.
The Football Association of Indonesia (PSSI) suspended football matches of Indonesia's top league, BRI Liga 1, for one week.