Israel's Iron Dome anti-missile system shot down three missiles fired from neighbouring Sinai late on Wednesday, the Israel Defence Force (IDF) said. Up to seven are thought to have been launched during the attack - in which no one was hurt - in total.
Gazan media reported that Isis, rather than Hamas, was responsible. Isis' official media channels confirmed the group was behind the attack later on Thursday.
The branch of the jihadist group based in restive Sinai province in Egypt is believed to have attacked Israeli targets multiple times in the past.
As well as the Sinai rockets, Israel has been hit by projectiles launched from Gaza this week, and in what the IDF described as not unusual "spillover" from the Syrian civil war, several rockets landed in the Golan Heights.
The IDF struck a target in the Syrian Golan in response.
The incident in Eilat marks the first time the Iron Dome has intercepted rockets aimed at the city since the 2014 war against Hamas.
As of Thursday morning, police had lowered Eilat's threat level back to normal.
Also on Thursday, Palestinian officials said that two people had been killed in a pre-dawn airstrike whilst smuggling goods through a tunnel linking Gaza to the Egyptian Sinai.
The Israeli military had no immediate comment on the claims.