The 21-year-old had made the switch to the Weserstadion from Hertha Berlin ahead of the 2012-13 season.
Strebinger was a prominent member of Werder's Under-23 side last term, though a long injury lay-off has curtailed his progress this season.
That has not deterred Werder from extending the Austria Under-21 international's contract, however, and the rookie 'keeper will now remain at the club until at least June 2017.
"I feel very comfortable with Werder," he told the club's official website. "I now have the chance to take another step forward. My goal is of course to play a good role in the Bundesliga with Werder."
Werder sporting director Thomas Eichin added: "Richard has developed very well over the past two seasons with us."
Strebinger's contract extension follows the news that fellow goalkeeper Sebastian Mielitz will depart at the end of the season.
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