According to police, several people had turned up to the game with batons and knives. At least nine people have been arrested.
“Athletic Club shows its strongest rejection of the violence generated around football.”
Footage of the clashes showed supporters aiming fireworks at each other on the streets.
David Vilumbrales, an Athletic supporter, tweeted a video from the scene saying: “Several injured in Bilbao. We were attacked by the Spartak ultras with golf balls and bottles and the ambulance does not arrive.”
“I was caught by surprise,” Vilumbrales told CNN, adding that fireworks, bottles, and golf balls were all thrown by Spartak “ultras.”
“I wanted to go to San Mamés Stadium on the safest street, Alamedo Urquijo, and I ran into a pitched battle all-against-all without police.
“Everything was very confusing and the police did not distinguish Athletic Bilbao’s fans from the Spartak because they all wear the same colors. The ultras were prepared in groups of 30 people and attacked us three times.”
Spain’s Prime Minister Mariano Rajoy, offered his condolences to Garcia and his family on Twitter.
CNN has contacted Spartak for comment.
In a statement, UEFA said it “strongly condemns the violent clashes which occurred on Thursday night.”
“We are in contact with local authorities to obtain further information on these incidents
“UEFA sends its sincere condolences to the family and colleagues of the police officer who passed away tonight. “
Spain’s Football Federation has announced plans for a minute’s silence at all upcoming matches.
Meanwhile, Real Madrid captain Sergio Ramos tweeted: “Football, sport and society cannot remain indifferent to violence, fear and the loss of life. We must force change.”
Russia World Cup
The incident once again places a spotlight on Russian hooliganism ahead of this year’s World Cup which Russia is hosting.
Russian hooligans caused trouble during the 2016 European Championship finals in France, clashing with rival supporters.
Both Russia and England were threatened with expulsion from the tournament following clashes between rival fans in Marseille.
However, world governing body FIFA says it has has “complete trust in the security arrangements and comprehensive security concept developed by Russia.
“As demonstrated during the FIFA Confederations Cup last year, Russia’s already high security standards have been adapted to meet the specific needs of such major sporting events,” said a FIFA statement.
Earlier Thursday, German police said they had arrested a Russian football hooligan for attacking an England fan during Euro 2016.
The suspect was arrested en route from Moscow to Bilbao where he was traveling to watch the game between Athletic and Spartak.
Spartak won the game 2-1, but Athletic progressed to the last-16 courtesy of a 4-3 aggregate victory.
The Europa League is UEFA’s second tier club competition.