Robben came on as a substitute for the Netherlands against his club on Tuesday. The friendly stemmed from a dispute over an injury he sustained at the 2010 World Cup.
Robben missed an extra-time penalty for Bayern in Saturday's Champions League final against Chelsea, which went on to win in a shootout.
Chairman Karl-Heinz Rummenigge said that after Saturday's loss some fans apparently were disappointed Robben appeared for only the Dutch "but that doesn't give anyone the right to boo our player."
He says Bayern "received many reactions from our fans who apologize to Arjen Robben in the names of those who booed."