Lewandowski was the subject of criticism from Hamann after Bayern lost 3-1 to Bayer Leverkusen last weekend.
The defeat saw Bayern lose ground to Borussia Dortmund in the Bundesliga title race.
Hamann criticised Lewandowski for being selfish in his approach and for his supposed theatrics during the game.
“I believe it is clear that he is an individualist,” he said.
“I think that Lewandowski is becoming a problem for Bayern.”
Lewandowski boasts 24 goals in 28 games for Bayern this season.
And the striker, who is set to come up against Liverpool next week in the Champions League, was far from impressed.
“I am always focused on my job, and cup games are always difficult to play,” he said after Bayern’s German Cup win over Hertha Berlin in midweek.
“We won that match, and I am not interested in what someone says about me.
“Even more so if that’s just flat-out stupid.
“I don’t think [Hamann] knows much about tactics.”
Indeed, a member of Lewandowski’s management team – Maik Barthel – also had a pop at Hamann.
“After the defeat against [Bayer] Leverkusen it does not help to attack players on this level as Mr Hamann has done,” he said.
“That he sees the Robert as the main cause says it all about his tactical understanding to me. Maybe he did not even see the game.”
Lewandowski is expected to start for Bayern Munich when they travel to Liverpool for the first leg of their last-16 Champions League clash on February 19.
Hamann won two Bundesliga titles with Bayern in the 1990s and helped Liverpool clinch the Champions League in 2005.