The wounded soldiers were reported in critical condition and taken to a hospital, said a security source.
There was no immediate claim of responsibility for the attack.
Sinai-based militants have stepped up violence against the state since the army ousted President Mohamed Morsi in July, killing more than 400 soldiers and police, according to the Foreign Ministry.
The Egyptian army has launched offensives against militants in the Sinai but the operations have failed to reduce the number of attacks on security forces. The violence has spread to the capital Cairo and other cities which also regularly witness protest rallies against the military-led government.
Security forces clashed later on Sunday with Morsi supporters, protesting at the campus of Al-Azhar University, a common site of unrest in recent months.
Police used tear gas and buckshot to disperse the protesters who had attempted to block traffic in the main street outside the university.
Security forces have mounted a tough crackdown on the Muslim Brotherhood, killing hundreds of its members and jailing thousands more.
RA/MB