The tunnel collapsed while policemen were planting explosives to destroy it.
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.
The Egyptian military had earlier launched security campaigns and demolished houses of terrorists in this area.
The militant attacks targeting police and military increased after the ouster of Islamist ex-president Mohamed Morsi last year.