It is understood the police officer who was policing the crowd surrounding the San Mames Stadium, suffered the heart attack after he recieved a head injury during an altercation with rioting fans of Atlethic Bilbao and Spartark Moscow.
Another four people were also taken to the Basurto University hospital in Bilbao on a night of tension.
It was feared that Russian Ultras had joined other fans and travelled to Spain without tickets and meeting at the Plaza Moyua at 6.30pm, when the first scuffles were reported. Five people were arrested - three Russian nationals and two Spaniards. Latest reports also claim that the atmosphere remains tense in Bilbao.
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After the game, Athletic Bilbao, tweeted: "Our heartfelt condolences to the family and companions of the deceased officer today. We do not know if they are all supporters of Spartak, but many of them are Russians", a spokesman for Ertzaintza told AFP.
The statement went on to ask fans not to "succumb to provocations and not enter conflicts with local residents".
Spartak won the match 2-1 but Bilbao progressed to the last 16 of the Europa League courtesy of a 4-3 aggregate win. The European soccer governing body typically hands down heavy fines to the clubs involved and stiff punishment to the fans, like banning suspects for life or forcing the teams to play behind closed doors.
Information from The Associated Press and Press Association was used in this report.