The servicemen were travelling to Cairo when the minibuses they were in was stopped at gunpoint in Al-Wadi al-Akhdar region which lies east of El-Areesh in north Sinai, Al-Alam reported.
The three captured policemen are from the Central Security Forces, the branch of the interior ministry used to quell protest.
The four other men belong to the armed forces. The two groups were travelling in separate minibuses, officials said.
"The kidnappers have not issued any demands yet," a security official said.
Local Bedouin leaders have been called in to mediate between authorities and the kidnappers. According to Bedouin sources, it is believed the kidnappers want the release of certain prisoners.