The soldier was killed when the militants fired on an army checkpoint near the north Sinai village of al-Gura, medics said, adding two other soldiers were wounded in the attack.
Following president Mohamed Morsi's ouster by the military, several militants have publicly threatened violence in retaliation.
Militants attacked a police base with rockets and attacked military intelligence headquarters in the border town of Rafa, security sources said.
A security source said militants were attacking army and police checkpoints in several towns in north Sinai.
Morsi, elected in June 2012 and deposed on Wednesday after mass protests, had himself ordered a crackdown on Sinai militants after an August 2012 attack killed 16 soldiers.
No group claimed credit for that attack. But Sinai based militants have taken responsibility for rocket attacks and cross border attacks against Israel.
