It did not, however, expel Tehran's ambassador or downgrade the level of diplomatic relationship with Iran.
The announcement comes after Sunni-led Saudi Arabia and Bahrain severed ties with predominantly Shiite Iran this week.
And the United Arab Emirates has recalled its ambassador and downgraded ties with the Islamic republic.
Bahrain, Kuwait, Saudi Arabia and the UAE are members of the Gulf Cooperation Council, along with Oman and Qatar.
The attacks "represent a flagrant breach of international agreements and norms and a grave violation of Iran's international commitments for the security of diplomatic missions and the safety of diplomats," the official KUNA news agency cited the foreign ministry as saying.
Around a third of Kuwait's native population of 1.3 million is Shiite.
Relations between Riyadh and Tehran were already strained over their support for opposite sides in conflicts in Syrian and Yemen, and were exacerbated over Saudi Arabia's execution of a prominent Shiite cleric.
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