It said a decision on the sanctions would be made "within the next few days," once evidence had been considered.
No action has been taken against England's Football Association, whose fans were also involved in the clashes on the third straight day of football-related violence in the port city. UEFA is responsible for incidents at match venues, but not in surrounding areas.
Dozens injured, 8 arrests
At least 35 people were injured Saturday, four of them seriously, said Mathieu Duroselle, a spokesman for Marseille police. The number included three officers who suffered slight injuries, he said.
Eight people were arrested, including British, Russian and French citizens.
The British government said in a statement Sunday that six British nationals were hospitalized and several others had received treatment.
"The UK Government is deeply concerned by the violence in Marseille last night, including reports that in some cases England fans were attacked by rival supporters," it said. "We condemn the violence and urge calm on all sides."
It said it welcomed UEFA's launching of an investigation into the violence at the stadium, and had offered to send additional British police to France ahead of England's next match, against Wales in Lens.