Israeli rescue services said the rockets fired from northern Gaza had exploded in the Israeli town of Sderot, wounding an Israeli woman and damaging a school.
In a separate incident earlier on Sunday, Israeli soldiers shot and killed two Palestinians also in the northern Gaza Strip.
Palestinian health workers said that the bodies of two men were brought to hospital after they were shot on Sunday near the site of a former Jewish settlement in Gaza.
According to an Israeli military spokesman, soldiers opened fire at two armed men as they approached a border fence with Israel.
The soldiers said they later found that both men carried grenades in addition to their guns, the spokesman said.
The Izz al-Din al-Qassam Brigades, the armed wing of Hamas, said two of its fighters had been killed in an exchange of fire.
Israeli soldiers often shoot at Palestinians who approach the electric fence that surrounds Gaza, arguing that they are trying to prevent armed infiltrations.
Hamas has controlled the coastal strip since routing forces loyal to Mahmoud Abbas, the Palestinian president, and his Fatah movement during factional fighting last month.
In a separate development, the bodies of three women bearing signs of torture were found in the Gaza Strip on Sunday morning.
The identities of the women were not immediately available.
The bodies showed signs of knife wounds and strangulation.
Health workers could not confirm the cause of death.