The IDF struck targets in the Gaza Strip on Tuesday afternoon in retaliation for the cross-border shooting earlier in the day in which Israel sustained its first casualty since the end of Operation Pillar of Defense in 2012.
The IDF employed the air force, tanks, and infantry to launch a response against six targets in Gaza.
Gaza hospital officials said three-year-old Hala Abu Sbeikha, was killed by shrapnel during the strike on the Bureij facility. She was standing with other family members outside their home in the nearby al-Maghazi refugee camp and her mother and two brothers were wounded, the officials said.
Three Palestinians were injured from the IAF strike in eastern Gaza, Palestinian news agency Ma'an reported.
The strike's targets were a site to manufacture weapons, and a terrorism infrastructure site in southern Gaza, a center for terrorism activity and a terrorism infrastructure site in central Gaza, and two terrorism targets in the north of the Strip had been hit, according to the IDF.
According to Ma'an, the targets included a military sites belonging to the Islamic Jihad's al-Quds Brigades between Khan Younis refugee camp and the city of Deir al-Balah and in the al-Atatra area of the northern Gaza Strip.
Officials from Hamas, the Islamic group which rules Gaza, and witnesses said IAF aircraft bombed the group's training camps in Khan Younis and al-Bureij. Witnesses said IDF tanks fired shells east of Gaza city.
"We identified an accurate strike of the targets. All of our planes returned to their bases safely," the IDF Spokesman said.
"Terrorist organizations have made it their goal to harm Israeli civilians. The IDF will act with determination against any element seeking to activate terrorism against the state of Israel. Hamas is the address and it is responsible," the IDF spokesman added.
During the IDF's wave of attacks, infantry soldiers struck targets with anti-tank missiles.
"We take a severe view of this, because it occurred on Israeli territory," a senior security source said of the cross-border shooting. He described the targets hit in Gaza as "terrorism infrastructure targets" belonging to Palestinian Islamic Jihad and Hamas.
"We're seeking a strong response, but also to contain this. We do not want to escalate, but we are on high alert in case this deteriorates," the source added. The IDF's Gaza Division has gone on high alert in case of a potential escalation.
"We're prepared for further steps if necessary," the source said.
Prime Minister Binyamin Netanyahu has issued a warning Tuesday evening to anyone who tries to test Israel's resolve by attacking its citizens.
"I wouldn't recommend testing us," he wrote in a Facebook post. "Whoever tried to got hit. Whoever tries to will get hit."
Spokesmen for the Palestinian Authority and Hamas condemned the IAF airstrikes on Tuesday evening, Ma'an reported.
Hamas spokesman Sami Abu Zuhri called the airstrikes a "cowardly crime," accusing Israel of targeting Palestinian families, while PA spokesman Ehab Bessaiso called for international intervention to stop the escalation on the Gaza frontier.
Concerned that "escalating violence" could result in "another cycle of bloodshed," United Nations Secretary-General Ban Ki-moon warned on Tuesday against further retaliatory strikes from Israel against the Palestinian territories.
Ban condemned "the killing of an Israeli civilian today as a result of cross border fire from Gaza, and the bus bombing near Tel Aviv on Sunday," his spokesman said in a statement.
"He also deplores the death of a young child in Gaza from Israeli retaliatory raids today as well as a number of Palestinian civilian casualties since Friday," the statement said, adding that the secretary-general hopes a two-state solution will end violence between Israel and the Palestinians "permanently."
Reuters and Michael Wilner contributed to this report.