"Four terrorists have been killed, including a suicide bomber who set off his explosives at one of the checkpoints attacked," the statement said, Xinhua reported.
It added that the security forces have frustrated terrorist attacks that took place in southern and western Arish on Tuesday night.
The attacks targeted three check points, according to the statement.
Some explosive devices, automatic weapons, hand-made bombs were seized, it added.
No group has claimed responsibility for the attacks yet.
Egypt's government has been battling extremist militants centered in northern Sinai since the military ousted Mohamed Mursi, who died last week after collapsing in court, in response to mass protests against his rule in 2013.
Some extremist groups, including the Sinai-based Daesh (ISIL or ISIS), that claimed most of the previous attacks, pledged revenge for his death.