Islamic State has claimed responsibility for a mosque attack in Kuwait that has left 25 people dead and hundreds injured.

A suicide bomber blew himself up during Friday prayers, in what is thought to be the first attack on a Shi'ite mosque in the country.

Kuwait's Prime Minister Sheikh Jaber al-Mubarak al-Sabah has described the bombing as an attempt to undermine unity in the country, where Shi'ite and Sunnis live side-by-side with little apparent friction.

"This incident targets our internal front, our national unity," he told Reuters after visiting those wounded in the attack. "But this is too difficult for them and we are much stronger than that."

Islamic State considers Shiite Muslims to be heretics, but Sunni Muslims have used social media to condemn the attack.

Kuwait's leading Sunni cleric, Sheikh Ajeel al-Nashmi, has described the bombing as a "criminal act aimed at sowing seeds of discord, and undoubtedly Shiites and Sunnis will foil the terrorists' plot."

Witnesses to the attack say the suicide bomber appeared to be in his 20s.

"He walked into the prayer hall during sujood (kneeling in prayer)," Kuwaiti parliament member Khalil al-Salih said.

"The explosion was really hard. The ceiling and wall got destroyed."

Three weeks ago, the government raised the level of security around mosques because of similar attacks in neighbouring Saudi Arabia.