The blast hit Al-Imam al-Sadeq mosque in Kuwait City, killing 25 people, the interior ministry said in a brief statement.
IS claimed what was the first-ever bombing of a Shiite mosque in Kuwait and the first terror attack in the Gulf state since January 2006.
The IS-affiliated group in Saudi Arabia, calling itself Najd Province, said militant Abu Suleiman al-Muwahhid carried out the attack on the mosque, which it claimed was spreading Shiite teachings among Sunni Muslims.
In the statement on the official KUNA news agency, the interior ministry said that 202 people were wounded in the unprecedented attack.
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A witness told AFP "dozens were killed and wounded," and pictures circulating on social media showed several bloodied bodies in the mosque amid debris.
A security official said "it is a suicide bombing."
Witnesses gave a similar account, saying a suicide bomber entered the mosque during the weekly noon prayers.
An AFP photographer who arrived at the site after the bombing said the area was cordoned off by police.
The television showed footage of massive destruction caused by the blast, and people posted online horrific pictures of the dead and wounded.
The Kuwaiti cabinet went into an emergency meeting to discuss the incident, as the interior ministry raised the level of alert and mobilised all security forces.
A number of hospitals in the oil-rich emirate declared states of emergency to deal with the wounded, while the central blood bank appealed for blood donations.
Kuwaiti Shiites make up around one-third of the country's native population of 1.3 million people.