Beckenbauer was part of the FIFA executive committee which voted to give the tournament to Russia in 2018 and Qatar in 2022, with the Qatari bid marred by allegations of vote buying.
"The apparent breach relates to Mr Beckenbauer's failure to cooperate with an Ethics Committee investigation despite repeated requests for his assistance," FIFA said in a statement.
"The case is now the subject of formal investigation proceedings being conducted by investigatory chamber member Vanessa Allard as chief of the investigation."
Former U.S. prosecutor Michael Garcia is investigating the decisions on behalf of world soccer's ruling body and is due to file his findings next month.
Britain's Sunday Times newspaper reported that Beckenbauer's former Exco colleague Mohamed Bin Hammam bribed fellow members to ensure Qatar would win the vote.
Bin Hammam has been banned from football for life over separate corruption allegations. Qatar has denied any wrongdoing.