The amount compared to a 2.9 million euro profit the previous season.
"Bayern are financially well positioned for the future," board director Karl Hopfner told the club's annual general assembly in Munich.
"Despite a difficult starting position - I remind you that we had no notable sporting success last season and faced an ongoing financial and euro crisis - we again recorded a profit," he said.
"We have also more than met UEFA's financial fair play criteria."
European football governing body UEFA's financial fair play rules, which aim to stop reckless spending on wages and transfer fees and come into full effect in 2013/14, say clubs must break even over three years.
The German record champions and four-time winners of the European Cup posted a turnover of 290.9 million euros compared to 312 million in 2009/10 with sponsoring and marketing revenues almost unchanged at 82.3 million.
Merchandising revenues grew to 43.9 million, up from 38.9 million last season.
Earnings before interest, tax, depreciation and amortisation (EBITDA) stood at 42.3 million, down from 61.2 million.
Bayern are still paying the bill for the construction of their Allianz Arena stadium which club officials expecting to have an additional 30 million euros available once it is paid off in less than 10 years.
