It was not the only dispute within the family.
Opposition MPs immediately launched a petition calling for the dismissal of both officials, holding them responsible for the country's crises.
"Political turmoil will not end without real, deep-rooted constitutional reforms," said Nasser al-Abdali, head of the private Kuwait Society for the Advancement of Democracy.
"This means keeping the ruling family away from running the executive management of the country on the way to achieving something similar to a constitutional monarchy," Abdali told AFP.
Unchallenged for more than 250 years, the ruling family in OPEC's fifth largest oil producer is accused of being embroiled in an intense power struggle that is stalling development.
"A dangerous struggle is taking place among members of the ruling family," liberal MP Abdulrahman al-Anjari said.
"I am afraid that if no real constitutional reforms are implemented, these disputes will spread like cancer. We have to contemplate adopting constitutional monarchy," Anjari said.
Mohammad al-Dallal, representative of the Islamic Constitutional Movement, the political arm of the Muslim Brotherhood, warned that "their (the family) infighting is damaging the country," and risking its very existence.
Independent political analyst Saleh al-Saeedi believes infighting within senior members of the ruling family has recently intensified.
"They are fighting for power, financial and economic influence and for control of the decision-making process... The intensity of the struggle has sharply increased," Saeedi told AFP.
"Fighting within the ruling family has moved to the street, the media and parliament and will be difficult to bring it back to its old (secret) form... the process appears to be out of control," he said.
Besides the emir, crown prince and the prime minister, members of the ruling family also permanently hold the key cabinet posts of defence, interior and foreign affairs.
Kuwait has been rocked by a series of political crises since Sheikh Nasser became prime minister in February 2006. Six governments have resigned and parliament dissolved three times.
Kuwait's version of democracy is also blamed for triggering disputes.
Often described as a "half democracy", the Kuwaiti parliamentary system, introduced about 50 years ago, is seen by many to have several serious shortcomings.
Under the constitution, many powers are concentrated in the hands of the emir who selects the prime minister, dissolves parliament and approves ministers and, above all, cannot be criticised.
Non-stop political wrangling has been blamed for stalling a $112-billion four-year development plan adopted in 2010, besides delaying mega projects including those in the vital oil sector.
Despite its massive surpluses of about $300 billion, 94 percent of Kuwait's income still comes from oil while almost three quarters of the gross domestic product is generated by the public sector.
MPs have repeatedly claimed widespread corruption in most public agencies which the government failed to halt.
According to the Berlin-based Transparency International, Kuwait slipped on the Corruption Perception Index from 35 in 2003 to 66 in 2009 before improving to 54 last year, but remains in last place among its Gulf partners.
Besides limiting the role of the ruling family, analysts and political groups have called for key reforms.
"We must have a law to legalise political parties and amend the constitution to boost popular participation," Saeedi said.
Political parties are banned in Kuwait but several groups act as de facto parties.
"Political disputes will continue in the country if these reforms are not adopted soon," Abdali said, while opposition MPs insist that ousting the prime minister is a pre-condition to end the crises.