Bulgaria Prime Minister Boyko Borissov called for him to quit on Tuesday after the racist abuse of England players in the Euro 2020 qualifier in Sofia.
Monday’s match, which England won 6-0, was stopped twice because of racist behaviour by home fans, which included Nazi salutes and monkey chants.
The BFU said the move “is a consequence of the recent tensions” but did not mention racism in their statement.
The statement said the tensions had created “an environment that is detrimental to Bulgarian football and the Bulgarian Football Union”.
It added that “Mihaylov expresses his firm readiness to continue helping in the development of Bulgarian football in every possible way”.
Earlier on Tuesday, the Bulgaria prime minister “strongly condemned” the fans’ behaviour and called for Mihaylov to resign “immediately”.
“After yesterday’s shameful loss of the Bulgarian National Team and given the bad results of our football, I ordered to end any relationship with BFU, including financial, until the withdrawal of Borislav Mihaylov from the post,” he added.