The missile defense system deployed at the southern city is undergoing assessments and being tested in locations around Israel, a military spokesman told United Press International.
The system was also deployed recently deployed in Safed in northern Israel
Police and soldiers searching in mountains near Eilat found the remains of the rocket. Two explosions had rocked Eilat Wednesday night, causing panic but no injuries, the army said.
Al-Qaida-affiliated groups operating in the Sinai claimed responsibility for the rocket firing.
The Iron Dome system, developed by Israel's Rafael Advanced Defense company, can intercept rockets with ranges of up to 70 kilometers (43.4 miles) in all weather conditions, shooting them down within seconds, officials say.