The kidnappers are reportedly demanding the authorities release from prison several fellow tribesmen, some of whom have been convicted of terrorism.
In March, Bedouin blocked access to the MFO's North Camp at al-Gorah for a day to press for the tribesmen's release.
They pulled back after giving officials a month to examine their demands.
The MFO is an independent force formed to monitor the borders between Egypt and Israel following the 1979 peace accord. It consists of military staff from 12 countries including the US and France.
Fiji provides an infantry battalion, whose mission is to observe and report all activities in the Northern Sector of Zone C, which includes the major border crossings at Rafah, Kerem Shalom and al-Awga/Nizzana.
"They were patrolling and we seized them by firing in the air," one of the kidnappers told the AFP news agency.
"They are with us now, and we want the liberation of all Bedouin prisoners." (BBC)