The Israeli military said it targeted Ahmad Zaanin, an operative in the Popular Front for the Liberation of Palestine, in order "to eliminate an imminent threat to the lives of Israeli civilians."
In Gaza, relatives and ambulance services said two militants were killed in the airstrike. The family identified Zaanin as one of those killed and the other was identified as his cousin who belongs to the Islamic Jihad group.
The military said Zaanin was behind several recent rocket attacks at southern Israel, as well as the shooting at soldiers and detonating explosives that targeted border troops.
In that attack, Palestinian militants fired four rockets at Israel, including two that landed several miles from Sharon's ranch in southern Israel shortly after his funeral.
"We will not hesitate to act forcefully against those who threaten to arm our security," Yaalon said.
After a period of relative calm, rocket attacks from Gaza into Israel have increased recently. Israel believes that most have been fired by smaller militant groups but holds the territory's Islamic Hamas rulers responsible for allowing the attacks to take place.