The strike blew up a house in the southern Gaza city of Khan Yunus.
The attack completely destroyed the two-storey house, killing two men who were inside and wounding at least 10, some in the house and some from neighbouring homes damaged by the explosion, medics said.
Residents identified the dead as a member of the al-Aqsa Martyrs Brigades, and his father, who they said was not a member of the group.
The Israeli army said that the house was used to store weapons and that the residents were warned to leave before the attack.
Late on Tuesday, Israeli soldiers fired at two Palestinian men, believed to be members of the al-Quds Brigades – the armed branch of the Islamic Jihad movement – but it was not immediately known if the men were dead or wounded, Palestinian security officials said.
An Israeli military official said that soldiers had fired after seeing two men crawling towards the barrier which separates Israel and the Gaza strip at the Kissufim border crossing.
At least 177 Palestinians and one Israeli soldier have been killed since June 28, when Israel launched operations to rescue a soldier captured three days earlier.