Othman Zain Nayef, a 26-year-old Kuwaiti national, had "used his office and computer to spread the extremist ideology of the so-called Daesh terrorist organisation", it said in a statement late Thursday, using an Arabic acronym for IS.
The ministry, quoted by state news agency KUNA, said he had allegedly confessed to being a member of the group's "electronic army" and to having hacked official websites "in friendly and sister states".
Kuwaiti authorities announced last month having dismantled three IS cells plotting attacks, including a suicide bombing against a Shiite mosque and hitting an interior ministry target.
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