Ukraine's National Police confirmed they had detained the individuals after an incident they described as "group hooliganism" on Velyka Vasylkivska street.
They added that "two injured foreigners" were taken to the nearest police station but that they refused to provide victim statements.
On Friday, the Daily Mirror published video footage showing a group throwing tables and chairs at people outside a cafe. The victims were reportedly Liverpool fans.
Further pictures showed one man, said to have been among the supporters targeted, with a bloodied head. It is claimed he was handcuffed by police after fleeing the scene before being released.
He told the newspaper: "We were just having dinner. They just stormed the place – they were throwing glasses and tables. It was terrifying.
"They wouldn't release us and we just wanted to leave. We did nothing wrong."
Police said the two individuals arrested also declined to give statements. An investigation into the incident is ongoing.