The 25-year-old, who also missed Germany's winning 2014 World Cup campaign through injury and has been linked with a move to the English Premier League next season, injured his knee cap in training on Friday.
"Season end and Euro out. Guendogan dislocated his knee cap in training," Dortmund said on Twitter. "Get well soon."
His injury could not have come at a worse time for national team coach Joachim Loew, who will now have to wait and see whether captain Bastian Schweinsteiger, another holding midfielder, will recover from his injury in time for the tournament in France starting on June 10.
"Obviously this is a setback for us all and especially bitter for Ilkay," said Loew.
"After missing Brazil through injury he will now also miss Euro 2016 for which he had a lot of expectations. He was in good form... and had played a central part in our planning."
"We all at the team wish him to come back onto the pitch soon," said the coach.
Guendogan was seen as a likely successor to 31-year-old Schweinsteiger in Germany's midfield alongside Toni Kroos.
The Germans have been drawn in Group C along with Poland, Ukraine and Northern Ireland.
Guendogan's injury is also a blow to his club, with Dortmund five points behind leaders Bayern Munich with two matches left to play in the Bundesliga and an outside chance at the title.
They also face the Bavarians in the season-ending German Cup final on May 21 in Berlin.
(Reporting by Karolos Grohmann; Editing by Hugh Lawson)
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