The 23-year-old has featured on nine occasions in the league for the Bundesliga champions this season.
Contento started in the 3-3 draw with Hoffenheim at the Allianz Arena on Saturday, with coach Pep Guardiola rotating his squad with the league title already assured and a UEFA Champions League quarter-final clash with Manchester United to follow.
However, the German is set for a spell on the sidelines, though Bayern did not specify how long he would be out for.
"Pep Guardiola will be without Diego Contento for Augsburg (ligament injury in his left ankle). Get well soon," Bayern posted on their official Twitter account.
Contento has risen through the ranks at Bayern, but has largely played second fiddle to the likes of captain Philipp Lahm and regular left-back David Alaba.
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