A Burnley fan was stabbed, and four others were injured, before the first leg of their Europa League play-off against Olympiakos in Greece.
The fan needed stitches to a leg wound and received medical attention at the stadium in Piraeus near Athens.
More than 900 Burnley fans travelled to Greece for the game; 22 were held by police for being drunk and disorderly.
Burnley lost the game, the first leg of the Europa League play-off round, 3-1. The second leg takes place on Thursday.
A statement from the club said: "The vast majority [of our fans] were once again impeccably behaved, with the coaching operation to transport supporters to the ground put in place by the club again a great success, as it was in the previous round in Istanbul.
"However, five of our supporters were unfortunately injured - including a person who received a stab wound to the leg - and received medical attention at the stadium.
"Those injured all travelled independently to the stadium, outside the organised travel operation."
The club added that the 22 fans detained were not arrested and were released later on Thursday night without charge.
The club said they were working closely with Olympiakos and local police to investigate the incidents.
Burnley, who went into the game unbeaten in their previous four qualifying games under manager Sean Dyche, have not been in European competition since 1966-67.
They beat Turkish side Istanbul Basaksehir and Scottish Premiership runners-up Aberdeen in extra time to set up the tie with Olympiakos.