Another 10 soldiers and seven civilians were wounded by the blasts outside the military intelligence headquarters in Rafah and at a nearby checkpoint.
A military spokesman blamed “Islamist terrorist elements” for the violence.
The military has launched an offensive in the Sinai to deal with a rise in attacks since it ousted Islamist President Mohamed Morsi in July.
Security fears intensified last week with a failed assassination attempt on the interior minister in Cairo. An al-Qaida-inspired group based in Sinai said it was behind the bombing that targeted Mohammed Ibrahim.
On Tuesday, troops backed by helicopter gunships raided militant hideouts in the villages of al-Mahdiya and Naga Shabana, south of Rafah, killing nine people, arresting 10 others and seizing weapons and ammunition, military officials said.
At least 29 militants are now reported to have been killed since military operations began in northern Sinai on Saturday.
Crackdown
The first suicide bomber drove a car at high speed into the two-storey military intelligence headquarters in the Imam Ali area of Rafah on Wednesday morning, burying a number of soldiers under the debris.
The powerful explosion shattered the windows of nearby buildings and sent a plume of smoke rising into the sky.
Shortly afterwards, another suicide bomber blew up an explosives-filled car next to an army checkpoint.
There were also reports that rocket-propelled grenades were fired.
The nearby border crossing with the Gaza Strip was closed in the immediate aftermath of the attack as troops searched the area for suspects, the state news agency reported.
The army has accused Mr Morsi of being too lenient toward militant activity in the Sinai, after he released Islamists from prison and vetoed military operations.
Egypt’s first democratically elected president was removed from office by the military on 3 July after mass street protests against him.
His ousting polarised Egyptian society and plunged the country into a new period of bloodshed and political uncertainty.
Two pro-Morsi camps in Cairo were broken up by security forces on 14 August, killing hundreds of his supporters. Dozens of security personnel also died in Egypt’s bloodiest day since the pro-democracy uprising two years ago ejected long-time President Hosni Mubarak.
Analysts say the army’s crackdown on Mr Morsi and his Muslim Brotherhood is adding impetus to militants in the northern desert.
Military deployments in the Sinai peninsula are subject to the 1979 peace treaty between Israel and Egypt.
An agreement between the two neighbours has been reached on Egyptian forces being bolstered by an additional mechanised brigade, additional tanks, commando units and Apache helicopters.