Tear gas was used on multiple occasions throughout the day by French police to disperse fans who were congregating in the city centre.
Police confirmed on Wednesday they had arrested 36 people, with 16 taken to hospital with injuries.
A UEFA statement read: "UEFA regrets the skirmishes which occurred in Lille last night. Police forces made several arrests and were quick to restore order and keep the situation under control."
England are playing Wales in nearby Lens on Thursday, while Russia suffered a 2-1 loss to Slovakia on Wednesday.
The incidents continued what has been a troublesome event for authorities and organisers, with violence threatening to overshadow the tournament.
Russia are already under a suspended disqualification which will come into force should there be a repeat of crowd disturbances inside stadiums, while England have been warned they could face similar sanctions, although they were not charged after the incidents at Stade Velodrome.