The ministry said in a statement late on Friday that the men were among a group of 26 who had received prison sentences from Kuwait's Supreme Court in June but they refused to turn themselves in.
They were accused of weapons possession and planning "hostile actions" inside Kuwait.
One Iranian man was tried in absentia and the rest are Kuwaiti nationals. Four men remained at large.
The case spurred Kuwait to shutter the Iranian cultural mission and reduce the number of Iranian diplomats stationed there last month, deepening a rift between the Gulf Arab states and Tehran.
The government says the terror group was uncovered in 2015.