The missile is believed to have been fired at an Islamic Jihad cell launching Qassam rockets at Israel.
The airstrike took place several minutes after the Palestinians fired five rockets at the southern town of the Sderot. One of the rockets landed near a WIZO day care center not far from the home of the town's mayor, Eli Moyal; two people suffered from shock.
Several mortar shells landed near the border fence, starting a fire in a hothouse in one of the Negev's kibbutzim. There were no reports of injuries.
IDF officials reported that immediately afterwards the army hit two Palestinians launching Qassam rockets at Israel. The two were operating south of the northern Gaza Strip town of Beit Hanoun.
Moyal told Ynet about the Qassam attack: "I was at home when I heard the explosion. I immediately entered the fortified room. We take the rocket fire very seriously. And again, like yesterday, a miracle happened. The Qassam landed next to an empty day care center. Yesterday, a rocket landed at a house's entrance and it was a miracle that there no injuries.
"The Southern Command chief spoke to me, but he is not the decision maker. We are still waiting for the government to act. It is true that there was a relatively calm period, but this calm is fictitious, and I believe that this calm is much more worrying than the recent rocket fire."
The Sderot task force, headed by city resident Alon Davidi, said in response to the rocket barrage, "On the evening when Israel's residents remember the murder which hurt Israeli democracy, Sderot's residents are abandoned by that same democracy, and are not entitled to the basic right of every democracy in the Western world – the right to live in security and without fear.
"We call on the prime minister to wake up from the dreams of concessions and order the IDF to launch a wide-scale ground operation to eradicate terror from Hamastan."
Ali Waked contributed to this report