The incident occurred in Bir Mutla, the ministry said, near the Ali Al Salem air base which hosts US air force personnel and planes, Reuters reported.
Kuwait has been a close ally of the US since American forces sided with the Kuwaitis in the Iraqi invasion in 1990.
Kuwait has provided intelligence, funding and the use of airfields for attacks by some members of a western-Arab coalition fighting Islamic State in Iraq and the Levant militants based in Syria and Iraq.
The US and its allies carried out a dozen strikes in Syria on Saturday, the US military said in a statement on Sunday.