Sports minister Nathi Mthethwa threatened on 14 October to intervene directly in CSA's affairs unless CSA provided him with reasons in writing why he should not get involved.
He set a deadline of 27 October. Government interference would put CSA at risk of sanctions from the International Cricket Council.
Sunday's resignations are likely to lead to the formation of an interim committee.
The latest move comes less than a month before a limited overs series against World Cup champions England.
Williams was made acting president following the resignation of Chris Nenzani in August.
According to CSA's tweet: "Mr Williams is deeply passionate about cricket and because of his love for the game he has resigned because this is the best way he can currently serve cricket."
CSA thanked Williams for his "loyalty and dedicated service".
In separate tweets, the resignation of four other non-independent board members and one independent board member were announced.
The resignations followed meetings of CSA's Members' Council, the overall policy-making body of CSA from which non-independent board members are elected.
The four non-independent directors stated they were resigning only from the board and would remain on the Members' Council, while Williams resigned from both bodies.
The resignations meant that only one non-independent and three independent directors remained on the board. It was not clear whether more resignations would follow.
In a statement following the tweets, the Members' Council confirmed the resignations of the non-independent directors and announced that Rihan Richards had been made acting president of the council. The statement did not mention the resignation of the independent director, Dheven Dharmalingam.
There was no immediate reaction from the sports ministry.