They "had no contact whatsoever with the local population" and the state is now free of the H1N1 virus, he said.
The health ministry announced on Saturday that officials had detected the virus among a number of US soldiers who were on their way through Kuwait, where the US army has a logistics base in support of its troops in Iraq.
"The American soldiers, whose names or ages were not disclosed, arrived in Kuwait on transit, they were examined and given appropriate medication," Ibrahim al-Abdulhadi, the Kuwaiti health undersecretary, said.
Some of the soldiers were quarantined in their base for treatment, the state news agency Kuna quoted a government official as saying.
The US embassy in Kuwait acknowledged the flu cases on Saturday, and said that the soldiers had not come into any contact with the Kuwaiti population.
The World Health Organisation (WHO) is poised to declare a full pandemic of the H1N1 flu virus, which has infected more than 11,000 people in 42 countries and killed 86.