Sheikh Salman Sabah al-Humoud al-Sabah, a member of the ruling family, was due to face the no-confidence vote on Wednesday following several hours of grilling last week in which lawmakers accused him of "complacency and mismanagement".
No confidence motions had in the past led either to the resignation of the minister facing a vote or the whole government, or brought about the dissolution of parliament.
Opposition candidates won nearly half of parliament seats in the 50-member assembly in November elections on the back of discontent over austerity measures to curb a budget deficit.
The International Olympic Committee (IOC) suspended Kuwait in October 2015, accusing the government of interference in its national Olympic committee.
The disagreement between Kuwait and the IOC is over a sports law which the Olympic body says is undermining the autonomy of sport in the country. Kuwait, however, is convinced the law strengthens the independence of sports bodies.
The ban means the country's Olympic committee and its athletes are not eligible for any funding from the IOC for the duration of the suspension and cannot take part in any IOC-linked event.
Last August, Kuwaiti athletes eligible to compete at the Rio Games had to do so as neutral athletes under the Olympic flag.
Veteran shooter Fehaid Aldeehani won the men's double trap event but he could not celebrate it as a Kuwaiti. Instead he was recognised as the first independent athlete ever to win a gold medal.
Kuwait's football federation has also been suspended by world soccer's governing body FIFA over government interference.
Last June, Sheikh Salman said Kuwait would sue the IOC in Swiss courts for $1 billion in damages over the country's exclusion from international competitions, calling it an "unjustifiable decision."
(Reporting by Sami Aboudi; Editing by Pritha Sarkar)
