The request deepens a dispute between the two branches of the ruling family over whether Shaikh Saad al-Abdulla al-Sabah, who took over on 15 January, should assume leadership of the state.
The cabinet is led by Shaikh Sabah al-Ahmad al-Sabah, the prime minister, who is the most likely contender for the post of amir if Shaikh Saad is relieved of his duties.
Shaikh Saad is due to take the oath of office in parliament on Tuesday. Under Kuwait's succession tradition, leadership of the country has to alternate between the two main clans of the Sabah family.
"A letter has been sent last night to parliament," the parliamentarian, who declined to be named, told Reuters.
"It asks parliament to hold a special session to look into activating the succession laws and to take a resolution that Amir Shaikh Saad is not able to rule on health grounds."
"It asks parliament to hold a special session to look into activating the succession laws and to take a resolution that Amir Shaikh Saad is not able to rule on health grounds"
A parliamentarian who refused to be identified
He said Jassem al-Kharafi, the parliament speaker, will meet MPs on Monday to discuss the government request. Any step to remove Shaikh Saad would require a two-thirds vote in the 50-member assembly and at least one member of the cabinet has to be present and vote.
Under the constitution, the cabinet can have a medical team examine the amir and report to parliament on his health.
Shaikh Saad, 76, took over as ruler of Kuwait after the death of his cousin Shaikh Jaber al-Ahmad al-Sabah.
Shaikh Sabah, the late amir's brother, has been de facto ruler for the past few years.
Shaikh Sabah is from the Jaber branch of the family, as was the late amir. Shaikh Saad is from the Salem branch.