No one in Gaza blamed Israel for the violence, indicating it was likely Palestinian infighting.
The late night blast killed Amar Musubah, a Hamas military field commander, and another Hamas militant, Eyad Al-Hia, medical officials said. A child and a fourth unknown individual also died.
Earlier, unknown assailants set off two bombs in Gaza City, killing one man.
The first explosion took place just after midnight outside the Al Jazera cafe. The cafe had been hit two other times this year in similar attacks presumably perpetrated by hard-line Muslims who target record shops and other sites they see as signs of Western influence.
The powerful blast wounded three people and killed the man who set off the bomb, Hamas officials said.
Another bomb exploded outside the house of a Hamas lawmaker, Marwan Abu Rass, not long afterward, causing light damage but no casualties, the officials said. An activist in the rival Fatah movement led by Palestinian President Mahmoud Abbas was arrested as a suspect.
Hamas officials said police were investigating all the blasts.
Gaza is the scene of regular bloodshed between Israeli forces and Palestinian militants, though the territory has been quiet over the past month because of the truce between Israel and the territory's Hamas rulers.
Gaza is also a common site of internal Palestinian violence between Hamas and Fatah. Hamas fighters defeated Fatah forces during five days of combat in Gaza a year ago, and tensions remain high.
Violence has also been blamed on Islamic fundamentalists who oppose what they see as signs of Western cultural encroachment.
In recent years, shadowy groups have firebombed internet cafes, music stores and Christian institutions. The bombings are typically carried out late at night and most have caused no casualties. But a Christian activist was murdered in one attack last October.
