Authorities said one rocket landed in an open area, one fell on a construction site and one landed on the city's outskirts, The Jerusalem Post reported.
Egypt has denied claims that the rockets were fired from the Sinai.
A number of residents reportedly were being treated for shock, officials said.
Israel Radio reported two rockets struck Aqaba, a resort in Jordan, a report Jordanian officials later said was false.
Police spokesman Micky Rosenfeld told the Post the airport in Eilat was temporarily closed for security reasons.
"We'll take additional precautions in the event of more rocket sirens," he said.
Defense officials said they would investigate why the Iron Dome anti-missile battery placed outside the city this month failed to bring down the rockets.
Eilat Mayor Meir Yitzhak Halevi said, to the best of his knowledge, the anti-missile defense system hadn't been activated.
In the Sinai, Egyptian security forces were searching the border area to investigate the Israeli claims.
"There is not yet any evidence indicating that these rockets were fired from Egypt," an Egyptian security source told the Post.