The row has been sparked after Nike made a lucrative offer to take over sponsorship of the national side.
The DFB says it is able to negotiate a new deal from 2011 – Adidas claim it extended its existing deal last August to run until at least 2014.
An Adidas statement said: “We are taking the matter to arbitration in order to achieve an objective decision in a timely manner.”
Reports from Germany earlier in the week suggested Adidas had upped its offer to $29m a year – while Nike has tabled a $660m eight-year with $132m in added benefits.
