The jets hit two training camps of the Ezzedine al-Qassem Brigades, the armed wing of Gaza's ruling Hamas movement, in the southern city of Rafah, Hamas security officials said.
A family of four, including an 18-month-old girl, were lightly wounded, after their vehicle was hit by shrapnel as they were driving by one of the targets, Adham Abu Selmiya, a spokesman for the Hamas-run rescue services, told AFP.
A third air strike hit an Islamic Jihad facility west of Khan Yunis, witnesses said.
The raids came after pre-dawn strikes against two other training camps of the hardline Islamic Jihad group.
The military had no immediate comment on the afternoon strikes, but said the earlier attacks "targeted a number of terror hubs... in response to recent rocket fire into Israel."
The air raids came after tensions rose along the Israel-Gaza border this week following clashes in which an Islamic Jihad gunman was killed and a rocket attack on the Israeli city of Beersheba that hit a house but caused no casualties.
It was the first rocket to strike the city since the devastating offensive Israel waged against Gaza in December 2008-January 2009 and prompted Prime Minister Benjamin Netanyahu to warn the territory's militants not to "test" the Jewish state.
That conflict killed 1,400 Palestinians, more than half of them civilians, and 13 Israelis, 10 of them soldiers.
Also on Saturday, a Palestinian man was shot and wounded in the leg as he collected gravel near the border fence in the northern Gaza Strip, Palestinian medics said.
Palestinians in Gaza frequently forage through the rubble along the territory's border with Israel, seeking construction materials which are otherwise in short supply because of an Israeli-imposed blockade.
A military spokesman said a group of suspicious people were seen approaching the border. When they failed to heed warning shots, "soldiers fired toward their legs and identified hitting one of them."
Israel imposes a 300-metre (yard) buffer zone along the length of the border as a "no-go" area where anyone who comes too close is liable to be shot at by soldiers manning watchtowers.