Lebanese security sources said that three rockets had been fired from southern Lebanon but two had landed inside Lebanese territory.
Lebanese sources say that Israel then fired at least six artillery shells.
Fouad Siniora, the Lebanese Prime Minister, denounced both attacks. No-one has claimed responsibility for the rocket firing.
A Lebanese source told Reuters that rockets had been fired from the area of Mansouri, south of Tyre, towards Israel.
A woman is reported to have been injured by flying glass in her home when the rocket landed near the Israeli town of Maalot near the Lebanese border.
Masad, an Israeli man, described hearing the Katyusha rocket hit his village.
“I was sleeping and I heard something like a bomb, I did not know what it was. I got up and saw, after a while, police around. I got out and saw something unbelievable, a Katyusha,” he said.
A spokesman for the Magen David Adom ambulance service said the three wounded had been taken to hospital.
The Israeli army said it had fired shells in response to the rocket attack.
The Lebanese prime minister denounced both attacks.
“The Israeli shelling is an unacceptable and unjustified violation of Lebanese sovereignty,” he said in a statement. “The rockets launched from Lebanon threaten the country’s security and stability and constitute a violation of UN Security Council Resolution 1701.”
Resolution 1701 ended the 2006 war between Hezbollah and Israel.
During the recent conflict in Gaza, rockets from Lebanon were fired into Israel twice.
Hezbollah denied responsibility for those rockets, suspected to have been fired by Palestinian militants.
Source: BBC News