Fuchs, who made his debut in a 4-1 defeat by Croatia 10 years ago, made 78 appearances, scoring a single goal against Greece in 2010.
Austria, who had previously taken part in the finals only as co-hosts in 2008 when they qualified automatically, were seen as dark horses when they arrived in France.
They never found their best form though and lost to Hungary, drew 0-0 with Portugal and slumped to a 2-1 defeat against tiny Iceland.
"The match against Iceland was my last game for the Austria national team. I am very proud of my years in the red-white-red and wish the team the best for the World Cup qualifiers," said the Austria left back in a video posted on Facebook.
"I'm very proud of the national team, the development over the last few years and that we have qualified for the European Championship finals on the playing field for the first time," added Fuchs, who plays for English Premier League champions Leicester City.
"We know that the performance in the final stages was not satisfactory. Despite this, the Euros in France were something special. I had the honour of leading the team on the field as captain and I really enjoyed the atmosphere."
The former Mainz 05 and Schalke 04 did not give a reason for his decision.
(Writing by Brian Homewood in Paris; editing by Clare Fallon)
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