Mediation efforts fail as Hamas forces clash with a powerful clan.
Hiyam Saker, a 51-year-old woman, was killed after she had been caught in the crossfire that erupted near the town of Rafah.
Eight other people were injured in the clashes that erupted in the town of Rafah. The breakdown of injuries was not immediately available.
Hamas and Islamic Jihad had different stories of why the fighting started.
Ihab al-Ghusain, a Hamas security spokesman, said the clashes erupted following a brawl between Islamic Jihad members and a Hamas supporter.
Islamic Jihad officials said the fighting began after Hamas members stopped one of their members in his car and refused to let him go.
Mutual captures followed and clashes spread around the town.
The tension in the south came as Hamas security were engaged in clashes with a large Fatah-affiliated clan in Gaza City.
Two people were killed, including a 13-year old, and at least 33 others were injured in those clashes.