In a statement carried by the official KUNA news agency, the ministry identified the attacker as Fahd Suleiman Abdulmohsen al-Qaba'a.
The ministry said that Qaba'a entered the country through Kuwait Airport at dawn on Friday, the same day of the bombing.
IS claimed the attack, which killed 26 and wounded 227 worshippers at the al-Imam al-Sadiq mosque in Kuwait City.
The ministry statement provided no further details about the bomber.
Earlier on Sunday, the ministry said that security services arrested the driver of the car that transported the bomber to the site of the attack.
Authorities have also detained the owner of the house where the bomber was staying.
He was described by the interior ministry as a Kuwaiti national who subscribes to "extremist and deviant ideology".
The driver, named as Abdulrahman Sabah Eidan Saud, was described as an "illegal resident" born in 1989.
Authorities on Saturday arrested the owner of the car, Jarrah Nimr Mejbil Ghazi, born in 1988, and also listed as a stateless person.