The tunnel collapsed as policemen were planting explosives to destroy it. The security forces are in search of two other policemen who went missing in the collapse.
The army has destroyed more than 1,813 tunnels since the ouster of president Mohamed Morsi last year, according to MENA news agency.
The network of smuggling tunnels connects the Sinai desert region with the Palestinian Gaza Strip, controlled by the Islamist Hamas movement.
The tunnels were used by militants to smuggle weapons, food and money to Gaza.
North Sinai has witnessed many violent attacks by militants since the January 2011 revolution that toppled the ex-president Hosni Mubarak.
The militant attacks targeting police and military increased after the ouster of Islamist ex-president Mohamed Morsi last year.