The alert comes over a planned parliamentary questioning by Sunni members of parliament of the information minister, a Shia.
"Frankly speaking, I am worried about this grilling," Shaikh Sabah al-Ahmad al-Sabah told Kuwaiti newspaper editors on Tuesday. "The media and MPs must tackle this questioning with wisdom so as it does not lead, God forbid, to a rift.
"There are enough sectarian moves in the region and we do not want to stir sectarianism in Kuwait," he said in reference to events in neighbouring Iraq.
Three Sunni lawmakers on Monday submitted a request to question Muhammad Abd al-Hasan for allegedly failing to "safeguard the principles, values and morals" of Kuwaiti society.
The request by Faisal al-Muslim, Awad Barad al-Anzi and Walid al-Tabtabai is due to be debated by the house on 3 January.
The questioning is unanimously backed by the Islamic Bloc which comprises the emirate's three main Sunni groups.
Abd al-Hasan is the only Shia minister in the 16-member cabinet.
The 12-page motion is centred on the minister's decision to issue permits for pop concerts and allow popular Arab singers to perform in Kuwait during the Muslim Eid al-Fitr feast in mid-November.
Shia, who form about one-third of the emirate's indigenous population of about 950,000, have been emboldened by events in Iraq, where the power of the Shia is on the rise after years of oppression under Saddam Hussein's Sunni-dominated government.
They have their own lower and appeals courts and were promised a supreme court to rule on the sect's personal status matters related to marriage, divorce, endowment and others, based on the Shia interpretation of Islam.
Kuwaiti Shia have five MPs in the 50-member parliament, down from six in the previous chamber.
In April, Shaikh Sabah was forced to intervene to defuse tension between the two communities in the oil-rich Gulf state after tit-for-tat statements and comments from hardliners in both camps through the media and in mosques.