The operation on Friday was aimed at ending what Egyptian officials claimed to be "smuggling" into the Palestinian territory, Al Jazeera said in a report also citing DPA news agency.
Gaza, administered by the Hamas movement, remains under a tight military blockade imposed by Israel and Egypt.
The government in Cairo last year began to destroy hundreds of homes on the Egyptian side of Rafah, which straddles both Sinai and Gaza.
The tunnels to Gaza are used to transport essential goods, such as clothing and other products.
The structures have frequently been targeted by both the Israeli and Egyptian militaries.
Cairo accuses Hamas of meddling in its affairs and supporting former President Mohamed Mursi, who was overthrown by the military, led by current leader Abdel Fattah el-Sisi in 2013.