Nkaissery, 68, a retired army officer, had held the position of cabinet secretary for interior and coordination of national government since late 2014.
"It is with deep sorrow and shock that we announce the sudden passing on of Interior CS Retired General Joseph Nkaissery," said a statement from Kenya's State House.
It said Nkaissery died "at Karen Hospital in Nairobi a few hours after being admitted for a check-up" without providing further details on the cause of death.
Nkaissery was a Member of Parliament from 2002 until 2014 when President Uhuru Kenyatta named him interior minister to replace Joseph Ole Lenku who was dismissed following a spike in insecurity and terror attacks in the country.
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