The blast, just south of the coastal city of Arish, wounded another 12 soldiers, several of whom were in critical condition.
Egypt has for years been fighting a Sinai-based Islamic insurgency.
The attacks have grown more frequent and deadlier since July 2013, when President Abdel-Fattah al-Sisi, then the defence minister, led the military ouster of Islamist President Mohammed Morsi, Egypt's first freely elected leader.
The insurgency has also spilled over into mainland Egypt, with a series of high-profile assassinations and bombings taking place in Cairo, the capital.
More recently, the militants have targeted Egypt's vital tourism industry, attacking a hotel near the Giza Pyramids and another in the Red Sea resort city of Hurghada.
No one was harmed in the first attack but three tourists, two Austrians and a Swede, were wounded in the second.
A local Islamic State affiliate claimed responsibility for the October 31 crash of a Russian airliner over Sinai, which killed all 224 people on board.
Moscow said the plane was downed by an explosive device smuggled on board.
The crash dealt a major blow to tourism, prompting Russia to cancel all flights to Egypt and Britain to suspend flights to the Red Sea resort of Sharm el-Sheikh, from where the Russian aircraft had taken off.
There was no immediate claim of responsibility for Wednesday's attack.