The US-based group SITE Intelligence Group, which monitors militant internet traffic, forwarded the Arabic-language claim to reporters today.
It wasn't immediately clear where IS was released the claim.
Sunday's shootings took place in the central Jordanian town of Karak. Hours after the initial attack, four gunmen were shot and killed by Jordanian security forces during a standoff at Karak Castle, a Crusader fortress and tourist destination.
The IS claim said that "four soldiers of the Caliphate" armed with machine guns and hand grenades carried out the attacks.