Those wounded were in their nearby home when the explosion went off. They were taken to hospital.
"We blew up the car remotely. There was a half a tonne of explosives" inside, an interior ministry spokesman, Hani Abdel Latif, told AFP. It was too dangerous to try to defuse the bomb, he explained.
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He added that those injured were cut by shattered window glass.
Tuesday's blast came during a nighttime curfew ordered since an October 24 suicide attack that killed 30 soldiers in a Sinai zone bordering the Gaza Strip. It was not clear what the car-bomb was targeting.
Attacks targeting security forces in the peninsula have occurred frequently since the army toppled Islamist president Mohamed Morsi in July last year. Most are claimed by jihadist groups reacting to crackdowns by authorities.
Egypt's Ansar Beit al-Maqdis jihadist group, which has carried out a string of deadly attacks from its Sinai stronghold, on Monday pledged loyalty to Islamic State group active in Syria and Iraq.