0330 GMT November 20, 2019
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, BBC Sport reported.
Monday's match, which England won 6-0, was stopped twice because of racist behavior by home fans.
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' behavior 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.
Before the match, Mihaylov had complained to UEFA about "unjust branding" after the buildup was overshadowed by fears England's players could be subjected to abuse.
The Vasil Levski Stadium was already subject to a partial closure for the match after Bulgaria was sanctioned for racist behavior during Euro 2020 qualifiers against Kosovo and the Czech Republic.
Uefa president Aleksander Ceferin said the "football family and governments" need to "wage war on the racists", after the abuse of England players.
UEFA told BBC Sport any action in response to Monday's events would have to follow on from a disciplinary committee, which in turn has to wait for a referee's report.
English FA chairman Greg Clarke, present at the Levski Stadium, said it was “probably one of the most appalling nights I have seen in football.”
British broadcaster ITV showed groups of men, dressed in black clothes, cupping their mouths and hurling abuse from the stands.
England manager Gareth Southgate informed the UEFA delegate after the first incidents and a public announcement was made, with play stopped.
The abuse continued and the match was again temporarily suspended by the referee under a three-step UEFA protocol for tackling abuse.
Sky Sports reporter Rob Dorsett said he had heard monkey chants on six occasions when England players Tyrone Mings and Marcus Rashford were in possession of the ball.
“I heard one fan clearly shout ‘Hey, monkey’ as Mings passed the ball,” he said.
Mings said later that his senior debut had been “slightly overshadowed” but “ultimately we let the football do the talking.”
England striker Raheem Sterling added on Twitter he felt sorry for Bulgaria “to be represented by such idiots in their stadium.”
Southgate told reporters a ‘huge statement’ had been made by the protocol being implemented and by his players’ reaction.
“I don’t think that’s ever been a situation that’s happened before in international football,” he said.
“For me, an even bigger statement was the way our players played.
“We’ve got players that have been through something they should never have to experience but have actually come off with a smile on their face because of how they’ve played.
“They always want the story to be about football but they’ve also been part of something that I think will be bigger.”
Southgate said there had been a long discussion about the situation during the second temporary stoppage.
“We were very clear that if there was anything at the beginning of the second half we would have walked straight off and frankly I don’t think we would have gone back,” he added.
Bulgarian captain Ivelin Popov spent time talking to fans through the metal fence at the break but sporadic abuse was still heard in the second half.