According to the source, unidentified gunmen opened fire on Military Intelligence headquarters in Rafah, prompting security forces to return fire.
The attackers, however, managed to flee the scene unscathed.
The same site – situated near Egypt's border with the Gaza Strip – was hit by a car bomb last September, killing six soldiers.
A second attack on Tuesday targeted a military vehicle in the village of Al-Mahdiya in southern Rafah during a joint police-army raid aimed at arresting wanted individuals, the source said.
The shooting left no casualties and three of the attackers were arrested, according to the source.
Egypt's Sinai Peninsula has seen an uptick in violence against police and army personnel since the July 3 ouster of Mohamed Morsi, the country's first freely-elected president, by Egypt's military.
Within recent months, scores of police officers and soldiers have been killed in dozens of attacks, especially in the peninsula's volatile northeastern quadrant.