Martin Guzmán had been in office since late 2019 and led negotiations with the International Monetary Fund (IMF) over the restructuring of Argentina's debt.
He called for "a political agreement within the governing coalition" to choose his successor.
Argentina is struggling with 60% inflation and a weak currency, as well as global food and energy price rises.
Martin Guzmán stepped down after a week of economic turmoil, with the Argentine peso sliding against the dollar.
His departure leaves a big question mark over Argentina's future economic policy.
In a letter to President Alberto Fernández , Martin Guzmán hinted at internal divisions within the government.