“We can confirm that a Basque policeman died Thursday,” said a press spokesman for the Ertzaintza regional police.
However, he refused to comment on Spanish media speculation that he had died as a result of the fighting which took place before the game.
He added that an autopsy would have to be performed before they were in a position to comment on the cause of death.
The deputy minister for security at the Basque regional government, Josu Zubiaga, told Cadena Ser radio that pending the “forensic reports, everything seems to indicate that there was no violent contact that may have resulted in the death”.
More than 500 police officers had been deployed for the high-risk return leg of the tie.
Earlier in the evening, police made a number of arrests as the violence and injuries escalated.
“Five people have been arrested. We do not know if they are all supporters of Spartak, but many of them are Russians,” a spokesman for Ertzaintza told AFP.
The trouble began as Spartak ultras arrived at the San Mames stadium in Bilbao for the game.
Some lit and threw smoke bombs and garbage cans before police charged at them.
Spartak won the match 2-1, but Bilbao went through 4-3 on aggregate.