Mr Beckenbauer is being investigated along with three other members of the competition's organising committee.
The four are suspected of fraud, criminal mismanagement, money laundering and misappropriation.
Mr Beckenbauer, who headed the bid in 2000, has previously denied corruption.
"Today I was interviewed as part of a long scheduled hearing by the Swiss federal prosecutor," Mr Beckenbauer, 71, said, adding: "I answered his questions."
The former Germany captain said he would not share more details of the case "out of respect for the prosecutor's office".
The Swiss attorney general's office told the Associated Press news agency that Mr Beckenbauer had been "co-operative".
The investigation into allegations that four members of the 2006 World Cup organising committee were involved in fraud and money laundering began in 2015.
The other three suspects under criminal investigation are former presidents of the German Football Association (DFB) Wolfgang Niersbach and Theo Zwanziger, and former secretary-general of the DFB Horst Rudolf Schmidt.
Tax authorities raided the DFB headquarters after it emerged that a secret payment of 6.7m euros (Â£4.6m; $7.2m) was made to Fifa in 2005.
The case first made headlines in October 2015, when German news magazine Der Spiegel accused Germany of using a secret slush fund to buy Fifa votes in support of its bid to host the 2006 World Cup.
The money allegedly came from the late Robert Louis-Dreyfus, who in 2000 was head of German sportswear giant Adidas.
It was allegedly provided at the request of Mr Beckenbauer, who led the committee seeking to secure Germany's right to host the event.
He has previously admitted to making errors in relation to the bid but has denied deliberate wrongdoing.
Mr Beckenbauer played his first World Cup for West Germany in 1966 in England and captained the team to victory as hosts at the 1974 tournament.
The former defender went on to manage French side Marseille and German giants Bayern Munich.
German football legend Franz Beckenbauer has been questioned by Swiss prosecutors over suspected corruption linked to the 2006 World Cup.