Maj. Gen. Gamal el-Baie, director of investigations for the south Sinai area, said Bedouin gunmen took the hostages to try to pressure the government into releasing two of their relatives, arrested on suspicion of dealing drugs, The New York Times reported.
It remained unclear whether the Egyptian government had met the demand.
Officials had been in discussions with tribal leaders in the area in an attempt to get the hostages released, the Interior Ministry said.
The minivan was attacked in the town of St. Catherine, a tourist hub near Mount Sinai, police said.
The abduction came just days after 24 Chinese workers and a translator were kidnapped by Bedouins en route to a military-owned cement factory, CNN reported.
Bedouins Tuesday blocked a road and kidnapped the workers, asking that the Egyptian government release prisoners.
The Chinese hostages were released a day later.