The security sources said a soldier was killed and two were wounded when a police station in Rafah on the border with the Gaza Strip came under rocket fire early on Friday.
The police post is close to the local headquarters of military intelligence.
Earlier, attackers fired rocket-propelled grenades at army checkpoints guarding El-Arish airport, close to the border with the Gaza Strip and Israel, in the latest of a string of security incidents in the region, the sources said.
It was not clear whether the attacks were coordinated and in reaction to Morsi's removal.
Egypt has struggled to control security in the region since the ousting of former dictator Hosni Mubarak in 2011.
On Thursday night, Eilat residents in the occupied lands reported hearing explosions in the area, sparking fears of a rocket attack, however police had not located any fallen projectiles.
Two blasts were heard at around 9:30 p.m. throughout the southern city, according to witnesses, but the red alert rocket warning siren was not triggered nor were there any reports of injuries or damage.
Israeli regime’s security forces launched a search of the area but said they could not confirm what caused the blast.