Police said a landmine went off as a bulldozer was trying to dig a tunnel to lay a gas pipeline, immediately killing its driver, Ibrahim Khadir al-Sabky.
They said the explosion occurred around 7:00 pm local time (1600 GMT) on Monday some five kilometres south of Dahab, a resort town on the Red Sea.
A second explosion occurred when a military team arrived to clear from the area landmines that were believed to have been planted during the 1967 Middle East war with Israel.
Two officers, Lieutenant Colonel Omar Mohammed Ali and Sergeant Abdel Rahim Taha, died in the second explosion, police said on condition of anonymity, because they are not authorised to give statements about military affairs.
Saeed Eissa, head of the medical emergency unit in Southern Sinai, said that two other soldiers were badly wounded.
He said they were taken to a hospital in Sharm el-Sheik for treatment.
Millions of land mines are believed to have been planted during the Israeli occupation of the desert peninsula that ended in 1980 after Egypt signed a peace treaty with Israel.
Police officials in Cairo said the ministry of interior was sending a team to the Sinai to investigate.