According to Kuwaiti diplomatic sources, who asked to remain anonymous, the number of Iranian diplomats in Kuwait will be decreased from 14 to nine, and the diplomats will be granted 45 days to leave the country.
Iranian "military, cultural and trade" missions were also closed and joint cooperation committees between the two countries suspended.
The row comes as Kuwait attempts to mediate an end to the Gulf's worst diplomatic crisis in years, after Saudi Arabia, Bahrain, Egypt and the United Arab Emirates cut ties with Qatar over accusations it supports "terrorism", an allegation Doha rejects as "baseless".
The state-run Kuwait News Agency announced in a brief statement that the Iranian ambassador in Kuwait, Ali-Reza Enayati, had been informed of the decision.
The official offered no further details and Iran has denied any involvement in the cell or the case.More news: Chipotle reopens restaurant that made customers violently ill
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In response, Iran summoned the Kuwaiti charge d'affaires to protest the Arab state's restrictions on the Iranian mission.
Saudi Arabia and its Arab allies are deeply mistrustful of Iran and many, though not Kuwait, have severed ties with it.
KUNA said on Thursday the move is related to the case of a "terrorist" cell broken up in 2015 that authorities allege had contacts with Iran and Hezbollah.
The only Iranian member of the cell was sentenced to death in absentia by the lower court early previous year.
It also lowered the life sentence for another man to 15 years in prison, and sentenced several others previously judged "not guilty" to 10 years.
The supreme court, whose rulings are final, overturned their acquittal on June 18 and sentenced them to between five and 15 years in prison.