In an interview with Switzerland's Blick newspaper on Sunday, Blatter suggested the vote for the host of the 2006 World Cup had not run smoothly and he suspected malpractice.
However, Beckenbauer, who was head of the organising committee for that tournament, was unhappy with the comments.
"I cannot understand the remarks and suggestions of Sepp Blatter," he said.
Blatter suggested the vote had been fixed to favour Germany over his own preference of South Africa.
Germany eventually won the right to host the tournament by 12 votes to 11, with New Zealand's representative of the Oceania confederation abstaining.
"When we talk about a World Cup being bought, I remember back to 2006 where, at the very last moment, somebody left the room and, instead of having a vote of 10-10, it finished 10-9 for Germany," said Blatter.
"I am pleased because I did not have to cast a deciding vote but for somebody to suddenly leave the room - maybe I was too kind or too naive at the time."
When asked if he presumed the vote had been fixed, Blatter said: "I don't presume anything, I am stating facts."
Those facts, according to Beckenbauer, are flawed.
"He has even got the result wrong," he said in Germany's Bild newspaper. "It was 12-11 and not 10-9.
"And what was decisive was that the eight Europeans all united behind us and voted for us."
The president of Germany's Football League, Dr Reinhard Rauball, has called for Blatter to step down as a result of the ISL bribery scandal which has recently come to light, but Blatter has ruled that out.
"It is nothing new that people want rid of me," said the Swiss.
"Sometimes it is the British media, then the American and then the German.
"The truth is, Rauball called me last Friday and told me that I should resign.
"I told him that it is not as easy as he imagines. The fact is, I have been elected by the congress.
"No club will decide whether and when I leave."