Rocket-propelled grenades killed the soldier at an Egyptian base near Rafah, the Palestinian Ma'an News Agency reported.
The other soldiers were injured when militants attacked eight army checkpoints in el-Arish, Sheik Zuweid and Rafah.
U.S.-made ballistic shells were fired Sunday at a security building in north Sinai, Egypt's Ministry of Interior said.
Three suspects were detained in that attack.
Late Sunday, a police station in el-Arish was hit by a bomb but no injuries were reported.