The Egyptian Health Ministry said seven other soldiers were injured in the attack, three of them critically, The New York Times reported.
The attackers commandeered armored vehicles afterward and tried to cross over into Israel, the Times reported. An Israeli military spokesman said one vehicle blew up at the border and a second was struck by the Israeli air force, the newspaper said.
No group had claimed responsibility for the attack in the northern Sinai Peninsula.
However, the Times said an unidentified Egyptian security official told state television militants from Gaza and others operating within the Sinai were to blame, though he provided no evidence.
Hamas spokesman Mahmoud el-Zahar told the Arab-language broadcaster al-Jazeera the Islamist group played no role in the attack.
State media reported Egyptian President Mohamed Morsi summoned the country's senior generals to discuss the situation, the Times said.
There were other reports of additional fighting about 12 miles from the border, the newspaper said.