The sport's European governing body UEFA and Marseille have launched investigations into the incident which led to the defender's dismissal for violent conduct before kick-off.
UEFA's Control, Ethics and Disciplinary Body will discuss the case at its next meeting on November 10.
Under the governing body's rules for misconduct of players and officials, Evra is potentially facing a minimum five-match ban.
A statement on Marseille's website said: "A professional player must keep his cool, face provocations and insults, as hard and unjustified as they are.
"Similarly, the club can only condemn by definition any destructive behavior of a pseudo supporter who insults his own players."
The incident evoked echos of an incident in January 1995 when Manchester United's Eric Cantona launched a karate kick at a Crystal Palace supporter who had mocked the Frenchman from the Selhurst Park stands after he had been sent off.
Cantona was subsequently handed a nine-month ban by England's Football Association.
Former French international Evra, who played 81 games for France, had been named as a substitute by Marseille coach Rudi Garcia and was warming up to prepare for the game against Vitoria Guimaraes at the Estadio D Afonso Henriques.
But he became involved in a heated exchange with a group of fans in an area of the stadium reserved for around 500 supporters of the French club.
The 36-year-old then directed a high kick at one of the fans and, after stadium stewards quickly broke up the melee, the former Manchester United defender was sent off by the referee.
UEFA's live text commentary of the game said Evra was sent off in the "0" minute.
"Patrice Evra is the first player to be expelled before the start of a match in the history of the Europa League," tweeted statisticians Opta.
In 2015, leading French football writer Philip Auclair wrote of the relationship between the Ligue 1 club and its fans: "The history of Marseille ... has been marked by animosity and, at times, near-warfare between its owners and the ultras, who cannot be uprooted."
Marseille coach Garcia was also surprised by Evra's reaction.
"Pat has experience, and he must not react, it's obvious," manager Garcia told reporters. "Patrice is more than just an experienced player."
However, Garcia was scathing of the fan who goaded Evra, adding: "He's not a supporter of Marseille, because you can't insult your own players, you have to be behind all of us."
Evra, who has struggled to gain a regular starting place this season at Marseille, has played for a number of leading European clubs, including Monaco and Juventus.
During the 2010 World Cup, Evra, who was then captain of France, was involved in an altercation with fitness coach Robert Duverne.
He was dropped for the final group game and subsequently suspended after the tournament.
Six years ago, England's FA concluded Evra -- then playing for Manchester United -- was racially abused by Luis Suarez in a game against Liverpool -- at a match in October 2011. Now playing for Barcelona, Suarez was given an eight-game suspension.
It was a grim night for Marseille, who lost the game 1-0 and also had Boubacar Kamara sent off three minutes from time.
Garcia's team are second in Group I, two points behind leaders Red Bull Salzburg, after four games.