Military spokesperson Colonel Tamer el-Rifai says the shootout, which also wounded two militants, took place early on Wednesday morning after a militant wearing a belt of explosives attempted to "storm" the checkpoint. He gave no further details.
Security officials said the attack took place just outside the border town of Rafah and that the two conscripts died when the suicide bomber blew himself up.
The officials spoke on condition of anonymiity becaue they were not authorised to brief the media.
Egypt has for years been battling militants in northern Sinai, who are now led by a local affiliate of the Islamic State group.