Fakhfakh was appointed prime minister by President Kais Saied in January following general elections last year that ended with no clear winner and a fractured parliament.
The Prime Minister’s office said Fakhfakh’s resignation was aimed at preventing more political conflict.
“The decision has been made in the national interest and in order to avoid more conflicts between state institutions in the country and to uphold the principle of moralization of political life,” the office said in a statement.
State media reports quoted Fakhfakh as saying he hoped his resignation opened up “a new path for a way out of the crisis” for the President.
Several governments have failed to revitalize the economy and tackle unemployment, while the coronavirus pandemic has worsened the situation, leaving the country to rely on a loan from the International Monetary Fund.