An Iranian official, however, described them as fishermen whose detention was not related to any border violations.
One of the Iranian men was wounded after refusing coast guard orders to surrender, the ministry said in a statement published by the state-run Kuwait News Agency.
The Interior Ministry released a photo on its website showing nine of the men on their knees with their hands clasped behind their backs.
The arrests are likely to draw more accusations by Arab Gulf countries of Iranian interference in their affairs.
Iran's semi-official Fars news agency quoted Ali Hajatpour, deputy chief of Bushehr province's coast guard in southern Iran, as saying some Iranian fisherman were detained in Kuwait because of a "quarrel."
He was quoted yesterday saying the dispute happened on Kuwaiti soil and that "their detention was not related to a border violation".
The incident could further strain ties between Kuwait and Iran.
An appeals court in Kuwait recently upheld the death sentence for a Shiite citizen on charges of communicating with Iran and the Lebanese militant Shiite group Hezbollah to commit "hostile actions" against the country.
Kuwait has also staunchly aligned itself with Saudi Arabia in the kingdom's diplomatic spat with Iran.
Kuwait recalled its ambassador to Tehran in January after a mob there ransacked the Saudi Embassy in protest against the execution of a prominent Saudi Shiite cleric.
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