The deadly blast took place in the “Imam Sadiq” Mosque in a busy area to the east of Kuwait City.
A Kuwaiti MP, who saw the attacker, said the mosque was packed with some 2,000 people when there was a loud explosion, Reuters reported.
Emergency services were attending the scene, which was surrounded by clouds of black smoke and crowds of people milling around.
The So Called Islamic State of Iraq and the Levant group (ISIL) claimed responsibility for the attack.
Kuwaiti Prime Minister Sheikh Jaber al-Mubarak al-Sabah said the attack was an attempt to threaten national unity. “But this is too difficult for them and we are much stronger than that,” he added.
The attack is the first such bombing targeting Kuwaiti Shiites, who make up around one-third of the country’s native population of 1.3 million people.