The three Islamist deputies accuse Iranian cleric Mohammad Fali of offending Kuwait's predominantly Sunni Muslim population by insulting some of the Prophet Mohammad's companions, whom Sunnis revere.
The deputies wanted Prime Minister Sheikh Nasser al-Mohammad al-Sabah to cut short the cleric's visit to Kuwait.
The questioning would include not only the cleric's visit, but also allegations of corruption and the government's spending of public funds, according to a copy of the motion obtained by Reuters.
It said the MPs also intend to query the prime minister about what they say are inadequate social services in education, health and housing.
Kuwait's constitution grants each member of parliament the right to question government ministers. Deputies do not have to vote on the motion for the questioning to proceed.
Parliament has a history of challenging the government and has repeatedly grilled ministers over their conduct, which has resulted in several ministers resigning to avoid no-confidence votes.
Kuwait's ruler Emir Sheikh Sabah al-Ahmad al-Sabah dissolved parliament in March after a row between deputies and the cabinet. But tensions persist.
(Reporting by Rania El Gamal; Editing by Catherine Bosley)
