The blast occurred on Wednesday during a massive search for the group that bombed the Red Sea resorts over the past year, Egyptian security officials said.
“The explosion was strong and appears to have come from a land mine which blew up under the vehicle,” said one security source, who asked not to be named.
Several thousand police with dozens of armoured vehicles are taking part in the operation.
The explosion took place in the northeast region of the Sinai Peninsula, in an area south of the town of El Arish, the hometown of many in the group.
It was not clear whether the mine was planted recently or left over from past wars with Israel.
Parts of Sinai still have mines from the 1960s, when Israeli forces occupied the peninsula.
The security source said three police officers were wounded, but an Interior Ministry official, who also asked not to be named, put the number of wounded officers at six.
A search operation
The ministry official also said there had been clashes with suspects during the search, which began on Tuesday at dawn in the area of Mount Halal, 60km south of El Arish.
Two police officers were wounded in clashes.
Police suspect the group of mainly Sinai Bedouin of organising seven bombings that have killed 98 people in Sinai since October.
The biggest attack was in the Red Sea tourist resort of Sharm al-Shaikh on 23 July.
Three coordinated explosions killed 64 people. Most of the dead were Egyptians, but British, Italian, American and other foreign tourists were also killed.
Egyptian police say they have arrested at least eight members of the group. At least four members of the group have been killed, either in their own explosions or in clashes with the police this year.