The attack took place this morning on the road from Rafah to el-Arish, the regional capital of North Sinai, where security forces are battling Islamist militants.
The attack is believed to be the deadliest against the military since Islamist President Mohammed Morsi was deposed.
Six soldiers, three security officers and the driver were among the dead, the military said.
The soldiers were going home for their holidays.
Although no group has claimed responsibility, such attacks are a signature method used by militants linked to al-Qaeda.
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Egyptian military spokesperson Colonel Ahmad Ali offered condolences to the Egyptian people on the deaths. He said the injured were transported to military hospitals for treatment.
He also stressed that the Armed Forces would continue to fight "black terrorism" until it gets rid of the "advocates of sedition and darkness".
Egyptian Cabinet spokesperson Hani Salah-al-Din also condemned the suicide attack.
He said the government was considering all options available to deal with such acts and to prevent their recurrence.