No damage or injuries were reported.
Several people were treated for shock, Israel Radio said. Unnamed Israeli security officials estimate at least one rocket was fired from the Sinai region, in an area where the Egyptian army is operating against terror groups. Channel 2 reported three rockets were fired at the Israeli city.
Hours after the incident, Israeli soldiers and security forces were still searching for the site where the rocket exploded, the radio said.
Al-Qaida affiliated Salafist group Ansar Bayit al-Maqdis claimed responsibility for the attack, which it said was in retaliation for the deaths of four of its Jihadist operatives, killed Friday in northern Sinai in a drone attack, Israel Radio reported.
Shortly after another group called the Mujahedin Shura Council in the Environs of Jerusalem who operate in Gaza also claimed responsibility for the rocket attack, Ynetnews.com said.
Egyptian security sources Friday said Israel struck a terror group on the verge of firing a rocket at Israel. There was no official comment in Israel to counter the claims but Israeli Defense Minister Moshe Ya'alon told Israeli media Saturday the Egyptian army "is fighting first and foremost to protect Egyptian civilians, as well as Egyptian sovereignty. We will not allow rumors and speculations as they developed over the past 24 hours, to harm the peace agreement."
The Salafist group Tuesday warned Eilat and other Israeli cities will no longer be able to enjoy the calm and the benefits of tourism and a thriving economy.
"The Jews will pay the price of the blood of the Jihadist operatives who were killed," the radio quoted a statement released by the group as saying.
Shortly after 1 a.m., residents in Eilat woke to the sounds of a siren and two loud explosions in the city. Locals and tourists were ushered into bomb shelters. The incident occurred at the peak of the summer vacation season, at a time the city's hotels are enjoying full occupancy.