Domenico Scala: Fifa`s independent audit committee president resigns
The council replaced the Fifa executive committee in the aftermath of a corruption scandal at the organisation.
Committees had been "deprived of their independence", said Scala.
Fifa said the Swiss "has made unfounded claims which are baseless".
Scala says he is "consternated" by a decision that makes it possible for the council to "impede" investigations by either dismissing committee members or "through the threat of a dismissal".
This, he added, "undermines a central pillar of the good governance of Fifa and destroys a substantial achievement of the reforms".
"[This is] a wake-up call to those persons who genuinely advocated for implementing reforms," he said.
Fifa, which accepted Scala`s resignation and installed his deputy Sindi Mabaso Koyana as acting chairman, insists the Swiss has "misinterpreted the purpose of the decision taken" by its congress.
It added in a statement: "The decision was made to permit the council to appoint members on an interim basis.
"In addition, the measure allows for the swift removal of members who have breached their obligations.
"The council fully respects the independence of the audit and compliance and the ethics committees, and any suggestions to the contrary are without merit."
Scala has played a key role in pushing through reforms after the scandals that prompted the departures of former Fifa president Sepp Blatter and Uefa counterpart Michel Platini.
Blatter, who had led Fifa since 1998, stood down last year and was later suspended from football for six years for breaching ethics guidelines.
Platini announced earlier this week he would be stepping down after failing to have a six-year ban from football overturned by a Court of Arbitration for Sport panel.
The first Fifa congress led by new president Gianni Infantino, who succeeded Blatter in February, took place in Mexico City on Thursday and Friday.
During the congress, Fifa elected its first female secretary general with the appointment of Senegal`s Fatma Samba Diouf Samoura.
She succeeds Jerome Valcke, who in February was banned from football-related activity for 12 years.