The explosion happened 200 metres from its military target, "when an Egyptian soldier used a tank to stop the vehicle", according to the army statement.
The victims – three men, two women and two children – "happened to be in the area in front of the ambush during the blast," the statement added, without saying when the incident happened.
"The explosion was large, carrying about 100 kilogrammes of high explosives," an army spokesperson said in the statement.
Egypt's military is battling a local affiliate of the Islamic State group that has waged a deadly insurgency in the northern Sinai, killings hundreds of members of the security forces.
At least 30 militants were recently killed by Egyptian forces during several days of security operations involving the army, air force and police in Sinai.
Five others were arrested as Egyptian forces imposed a "tight siege" on the North Sinai provincial capital el-Arish and the cities of Sheikh Zuweid and Rafah, according to a military statement.
Since December, IS has also targeted Christians in other parts of the country, including in Cairo, killing dozens.
The extremists have threatened to carry out further attacks on Christians, who make up about 10 percent of Egypt's 90 million people.
Last year, a suicide bombing killed 26 people, mostly women and children, at a Coptic Christian church in Cairo.
In May, masked gunmen attacked a bus carrying Coptic Christians in southern Egypt, killing at least 28 and injuring 25.
Coptic leaders have been strongly supportive of President Abdel Fattah al-Sisi, despite his crackdown on opposition, the deaths of hundreds of protesters, and a perceived inability to keep Copts safe.
-- Sent from my Linux system.