The vote will be held on February 10 and 11 on the movement’s online platform, Rousseau.
The M5S had initially ruled out backing Draghi, but after meeting him on Saturday its leader Vito Crimi said he was open to considering supporting him on the basis of the policies he proposed.
Italy has been without a fully functioning government for almost a month since the centre-left coalition collapsed, forcing Giuseppe Conte to resign as prime minister.
Draghi was brought in by Italian President Sergio Mattarella last week to form a new national unity government to face the devastating health and economic crises caused by the coronavirus pandemic.
Draghi on Monday held the final round of talks with smaller parties and is set to meet the M5S, the Democratic Party (PD) and the far-right League on Tuesday.
He is expected to report back on Wednesday to Mattarella on whether he can form a government.
He would then need to present a list of ministers and take office with his cabinet following a swearing-in ceremony at the presidential palace — something that could happen by Friday.
The instalment of the new government would be completed by votes of confidence in the two houses of parliament, where Draghi would spell out his agenda.
