Hamas, the Lebanese paramilitary organization regarded by many countries as a terrorist organization, is involved in security along the border at the request of the Egyptian government.
The explosion occurred early Thursday as the suicide bomber, identified only as a Palestinian, and another person were arrested by Hamas forces near the Rafah crossing between Gaza and Egypt.
Several other Hamas members were injured in the blast, a spokesman for the Hamas-backed Gazan Interior Ministry said.
Thursday marked the first time a Palestinian conducted a suicide bombing against Hamas security, the Jerusalem Post reported, adding that the bomber may have intended to detonate his explosives at a location in Egypt.
The Hamas-affiliated Palestinian Information Center reported that 28-year-old Nidal Jumaa al-Jaafari, a member of Hamas' armed wing, died in the rare attack against Hamas.
A Hamas statement said the attacker was a "suicide bomber with extremist views," a possible suggestion that he was a member of the Islamic State, the Israeli news website Haaretz reported. Hamas has long been accused of offering shelter to IS militants.