Lebanese media reported that dozens of people remain trapped inside the building which was sheltering several families, some of whom had fled the Israeli bombardment of the Lebanese coastal town of Tyre.
Yasir Abu Hilala, Aljazeera's correspondent in Qana, said aid workers had only managed to pull out three people alive.
Efforts to get the wounded to hospital have been hampered as all roads around Qana have been destroyed by Israeli air strikes, he said.
The Israeli army has rejected responsibility for the deaths, saying that Hezbollah bore the blame because it used the village as a site for launching rockets.