The rocket, believed fired from a Katyusha rocket launcher, damaged an empty refrigerator warehouse, Jordanian officials said.
A second rocket splashed into the Red Sea near Israel, Jordanian and Israeli officials said. Aqaba borders Eilat, Israel.
Explosions were heard and flashes of light were seen in both cities, officials said.
Authorities sought to determine if the rockets, believed fired from Egypt's Sinai Peninsula, were aimed at Eilat, Ynet News reported.
The rocket attack is the first in the Eilat-Aqaba vicinity in 4 1/2 years. In 2005, rockets landed in Aqaba -- two nearly missing a U.S. Navy ship docked at the Aqaba port -- and near Eilat's airport.
A group linked with al-Qaida claimed responsibility for the 2005 attacks.