Mack, who is 55, will quit at the end of the month and Chief Financial Officer John Ramsay will take charge on an interim basis, the company said in a statement on Wednesday.
Shares were up 4.4 percent at 323.60 Swiss francs at 0840 GMT following the announcement, with traders saying the change could rekindle bid speculation.
But a source close to Syngenta said that, as Ramsay is not a member of the board and is unlikely to become one, the board's attitude towards a takeover was unlikely to change.
Syngenta, the world's largest maker of pesticides has been under pressure to boost shareholder returns after rejecting the possible deal with rival Monsanto.
A group of rebel Syngenta shareholders said the change could benefit the company.
"We welcome the decision because it shows that somebody takes responsibility," said Folke Rauscher, managing director of a group calling itself the "Alliance of Critical Syngenta-Shareholders".
"It opens up new perspectives in terms of exploiting all options to fully get Syngenta's potential back," Rauscher told Reuters. The group says it now has the support of more than 80 Syngenta shareholders since it was set up earlier this month.
The Swiss group's troubles were compounded last week when it reported third-quarter sales that fell more than expected.
"I believe that this is an appropriate time for the company to benefit from the perspectives of a new leader," Mack said in a company statement on Wednesday, calling current market conditions challenging.
"I wish John (Ramsay) every success in his new role," added Mack, an American who had been in the top job since 2008.
Analysts linked Mack's departure to Monsanto's spurned takeover bid as well as disappointing third-quarter earnings and said that the company should hire externally.
"In our view, it would be best to appoint an industry insider - but outside person - with a fresh viewpoint on Syngenta," Kepler Cheuvreux wrote in a note.
"We do not believe that just because of Mike Mack's decision to retire from Syngenta, Monsanto will develop novel short-term ambitions on Syngenta again."
Syngenta's shares dropped 23 percent on the day that Monsanto announced it was abandoning its pursuit of the Swiss company, and in the last month the shares have traded at between 288 and 322 Swiss francs ($301-337), down from 400 francs in August.
The Monsanto approach equated to a price of around 433 Swiss francs per Syngenta share.
In September the company unveiled plans to buy back more than $2 billion of stock to boost shareholder returns after rejecting Monsanto's takeover approach, and put its vegetable seeds business up for sale to fund the measure.