The foundation said in a statement Fintech, a U.S.-based investment fund owned by Mexican businessman David Martinez, had bought a 4.5 percent stake.
BTG Pactual Europe, a unit of the Brazilian investment bank controlled by billionaire financier André Esteves, purchased the remaining 2 percent.
The shares were sold at a price of 0.2375 euros per share. The bank's stock rallied 10.6 percent to 0.28 euros by 0824 GMT (9:24 BST).
The statement said the two buyers and the Monte dei Paschi foundation had committed to keeping a combined stake of 9 percent in the bank before and after a 3 billion euro capital increase due to be launched at the end of May.
Monte paschi
(Reporting by Silvia Aloisi)