Spierings steps down later this year.
Jones' criticism was in response to Fonterra's heavy capital losses, thought to be more than $1.3 billion, particularly in its China investments. Fonterra was created under special enabling legislation from an industry mega-merger in 2001 to be a national export champion.
Fonterra director John Monaghan had been selected as the new chairman.
Wilson declined to comment and a Fonterra spokesman said Monaghan would not be publicly commenting today.
Read more: Fonterra chair John Wilson's exit comes as shock to shareholder boss
The Fonterra Shareholders' Council, which represents Fonterra's 10,000-odd farmer owners, only learned of Wilson's retirement yesterday.
Council chairman Duncan Coull said Wilson's advice to him yesterday was a surprise and a shock.
Wilson, a Waikato dairy farmer who had been on the Fonterra board four terms, two of them as chairman, was required to seek re-election this year under the board's rotation system.
Nominations closed on Monday. Wilson will remain a director until the company's annual meeting in November in Hamilton when he will retire.
Jones last month said Fonterra should stop being political and instead focus on its business.
"They should focus less on interfering in politics and more on justifying the money they've lost overseas. I believe that they have become disconnected from the farming community."
Jones said he had suggested to Agriculture Minister Damien O'Connor it may be time to restructure Fonterra, which 17 years after its creation, still has about 80 per cent of New Zealand's raw milk market.
"The leadership of Fonterra, I believe, starting with the chairman, is full of its own importance and has become disconnected," Jones said at the time.
He said there was an absolute absence of accountability for the "enormous amounts of dough" that the current chairman had presided over.
"The CEO has gone, well that's only one party of the double-Dutch we've had to put up with in Fonterra over the last nine years. I thoroughly believe this ... that as the CEO leaves Fonterra, the chairman should in quick order catch the next cab out of town."
Spierings is Dutch.
"I've been bloody disappointed that Fonterra, in my view, the leadership has not accepted that there's a new Government and there is a new narrative and I've had a gutsful of them believing they are bigger than what they really are," Jones said last month.
Fonterra's share price fell 1c today to $5.16.