The game has reached the midway point with Bayern 1-0 ahead thanks to Robben's fourth-minute opener.
Robben broke the deadlock with a stunning volley following a corner kick.
However, the Holland star's night was over just after the quarter-hour mark.
He left the field in plenty of discomfort after being brought down by Augsburg goalkeeper Marvin Hitz.
Hitz received a yellow card, but a foul was not awarded because Robben had been called offside.