The roof of a house about 100 metres from Amir Peretz's home in the town of Sderot was damaged on Wednesday by one of three rockets that Islamic Jihad members said they fired into southern Israel.
The makeshift rockets are very inaccurate.
The Israeli army said only that the rockets had landed in a residential area in Sderot.
The attack was started a day after Israeli commandos, mounting the first ground raid in the Gaza Strip since Israel's withdrawal last year, killed three members of an Islamic Jihad rocket squad and a policeman who came to their aid.
Inspecting the damage at his neighbour's home, Peretz told reporters that the Israeli military, which shells rocket-launching areas in the northern Gaza Strip, would "find a way" to prevent such attacks.
Eli Moyal, the mayor of Sderot, told Israeli Radio: "Our luck is that the Palestinians don't know how to aim precisely.
"There are only two ways to stop this - either destroying the area where they fire the rockets from or controlling that area."
However, the Israeli military has been reluctant to start a ground offensive in the Gaza Strip, from which it withdrew last September.
Tuesday's incursion lasted five hours, and troops sneaked 3km into Gaza.
Israeli troops pounded northern Gaza with artillery fire in response to the latest attacks. No casualties were reported on either side of the frontier.
Islamic Jihad said the rockets were a response to Israeli raids and the killing of a senior group official in Lebanon on Friday.
An Israeli government source denied at the time that Israel had anything to do with the death.