The game could not begin on time as fighting between the fans took 45 minutes to bring under control with tear gas and police charges.
The game eventually kicked off around 45 minutes after it was meant to.
Clashes between rival fans started hours before the kickoff after around 15 000 Besiktas supporters arrived in Lyon, marching through the city centre and lighting dozens of flares.
"Disciplinary proceedings have been opened following the UEFA Europa League quarter-final match between Olympique Lyonnais and Beşiktaş JK (2-1), played on 13 April in France", the statement read.
The trouble prompted police involvement outside the ground with French authorities allocating the fixture as "high risk" and commandeering 500 police for the fixture - more than double the number for a normal match.
French fans spilled on to the field for their own safety as fireworks were set off and missiles thrown from an upper section of the stadium housing Besiktas supporters.
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Lyon president Jean-Michel Aulas was also seen urging supporters to calm down and return to their seats but following full-time the 68-year-old claimed there had been no choice but to "flee".
Up to 20,000 Turkish fans, the majority living in France or Germany, were intermingled among the 35,000 supporters of Lyon on top of the 3,000 fans from Istanbul situated in the visitors' stand.
The match was expected to kick off at 8.05pm, but Uefa spokesman Pedro Pinto tweeted that there would be a delay due to "crowd disturbances". "But it would be very risky for us to face this opponent with the same supporters as tonight".
Dortmund's game against Monaco in the Champions League quarterfinals was postponed and played on Wednesday.
Lyon waited until nearly time to score twice in two minutes.
Stewards looked to be injured from the violence as police and medics tried to safely take them away from the violence.
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