The statement from the terrorist group's media arm, Amaq, said four men carried out the attack.
"Armed with machine guns and hand grenades, they raided the gatherings of the apostate Jordanian security and the citizens of the crusade alliance in Karak," read the statement.
This is the first time ISIS has claimed an attack on Jordanian soil. The only other attack ISIS claimed was a June suicide attack at a military outpost at the border with Syria.
Jordanian security forces engaged in another gunfight in Karak on Tuesday, but the country's Public Security Directorate said it was unrelated to Sunday's attack.
The security forces surrounded a house where an unspecified number of wanted men were located, according to Petra, Jordan's official news agency.
Sunday's attack in Karak was the first time a civilian target was hit by a terrorist attack in Jordan in more than a decade.
After firing at police officers at two locations, gunmen moved into an ancient castle popular with tourists in the city of Karak, Jordan's PSD said.
Security forces surrounded the castle and an hours-long standoff ensued. The PSD issued a statement around 11:30 p.m. (4:30 p.m. ET) Sunday saying the siege had ended with four terrorists killed inside the castle.
Seven members of the security forces, two Jordanian civilians and a Canadian tourist were killed, the PSD said. Thirty-four people were wounded, including 15 members of the security forces, 17 Jordanian civilians and two foreign tourists.
"Jordan is strong and is capable of eliminating terrorism," King Abdullah of Jordan told the National Policies Council on Monday, Petra reported. The King also visited some of the injured from Sunday's attack.
Jordanian Interior Minister Salama Hammad said in a news conference Monday the gunmen had more attacks planned.
"In the light of the number of explosives and weapons found, the target wasn't just Karak," the interior minister said, according to local media.
It all started with a report to the police from the gunmen's neighbor, who said he smelled gunpowder, Hammad said. As police investigated, a shootout began, killing one police officer as the gunmen fled from the nearby town of Qatranah to Karak, ending at the castle.