Bayern said on their website that a routine pre-season exam had shown that Robben had a torn muscle in his left thigh, adding he had suffered the injury shortly before the World Cup.
The 26-year-old missed the his team's first two group matches at the World Cup, but then played in the remaining five and helped the Dutch reach the final where they lost 1-0 to Spain after extra-time.
"This is a severe injury," club doctor Hans-Wilhelm Mueller-Wohlfahrt told the club's website.
"I find it irresponsible that this injury has not been precisely diagnosed and that they have let Arjen play.
"For my part, I offered to help with the diagnosis but this was not taken into account."
The Bundesliga club had initially issued an even more strongly-worded statement but quickly replaced it with a toned-down version.
Robben, who scored two goals at the World Cup but missed a superb chance to put the Dutch ahead in the final, was quoted as saying: "It's a shock for me to get a diagnosis like this on my return.
"I'm very disappointed, this absence is bitter for me and for the team."
Club president Karl-Heinz Rummenigge was also upset.
"Naturally, Bayern Munich are angry," he said. "Once again, we as a club must pay the bill after a player has been severely injured with his national team."
The club said they would take the matter up with the Dutch federation.
Former PSV Eindhoven and Chelsea striker Robben joined Bayern early last season from Real Madrid, where he had fallen out of favour.
He scored twice on his debut and went on to help Louis van Gaal's team win a Bundesliga and German Cup double.
They also reached the Champions League final, where they lost to Inter Milan.
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