Police faced problems before kick-off as well as a second incident after the match, which the Owls lost 1-0.
Both clashes took place near the Meole Brace roundabout, near Shrewsbury’s Montgomery Waters Meadow Stadium.
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The suspect who was arrested has since been released without charge. Police declined to confirm whether he was a home or away supporter.
Around 1,650 fans attended Wednesday’s Ligue 1 match after the club sold out their ticket allocation.
The crowd of 8,270 was Shrewsbury’s highest home attendance of the season and there was a visible police presence inside the ground to help keep order.
A “handful” of away supporters were then denied access to the match.
A West Mercia Police spokesman told The Star: “Police dealt with two separate incidents at the Shrewsbury Town and Sheffield Wednesday football match on Sunday January 2 involving supporters of both teams.
“The first was reported before the game near the Meole Brace roundabout opposite the New Meadow Stadium, where officers attended and dealt with the incident.
“The second happened after the game, still near the Meole Brace roundabout, where the fans shouted verbal abuse at each other.
“A man was arrested following the incident but has since been released and will receive no further action.”