Petkovic said he had no option but to drop Inler due to the 31-year-old's lack of match practice with Leicester City this season, though he said it had been a difficult decision.
"I'm very, very sorry for Gokhan. He is a great player and a great character," said Petkovic. "But I have to remain consistent in my acting and thinking."
"Competitive rhythm is one of the most important considerations for a squad in such an important tournament."
Former Swiss captain Inler, who played at Euro 2008 and the last two World Cups, has made only five appearances for Leicester in their English Premier League-winning campaign following his move from Napoli.
He did not complete a single game and has not played at all since December.
Petkovic also left out central defender Timm Klose due to a knee injury.
Switzerland, who reached the last 16 at the World Cup two years ago, meet hosts France, Romania and Albania in their first-round group.
Petkovic is under pressure after his team performed poorly in their friendlies in March, losing to Ireland and Bosnia without scoring a goal.
(Writing by Brian Homewood; Editing by Richard Balmforth)
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