An explosives-laden car was detonated by remote control near government buildings in the town of Rafah, on the border with the Palestinian Gaza strip, they said.
The blast went off around 10 metres (yards) from the bus transporting soldiers who were on leave.
Militants have stepped up attacks on Egyptian security forces in north Sinai since the ouster of president Mohamed Mursi in July, killing scores of soldiers and policemen.
The jihadist group Ansar Beit al-Maqdis (Partisans of Jerusalem) has claimed some of the deadliest attacks in Egypt since Mursi's overthrow, AFP reported.
Analysts say the group is inspired by Al-Qaeda, but Egyptian security officials claim it is derived from the now-banned Muslim Brotherhood, to which Mursi belongs.
The army has poured troops into the mountainous and underdeveloped peninsula to combat the growing militancy.