A second Israeli air attack targeted a Hamas police base in the town of Khan Younis in the centre of the strip and killed two Palestinians, a source said, without specifying if the victim had been a Hamas members. Three others were wounded in the attack.
Hamas claimed responsibility for the earlier rocket attack on Israel, which struck the Kfar Aza collective farm in the southern part of the country.
Israeli ambulance workers said the civilian killed in the rocket attack was a middle-aged man. Three other people were wounded.
Men belonging to the armed wing of Hamas regularly fire rockets and mortars into Israel from Gaza and, while the homemade rocket attacks rarely cause death or injury, they overshadow life in the border towns.
The last time an Israeli civilian was killed by cross-border rocket fire was on February 27.
The attack was followed by days of Israeli military action in the Gaza Strip which left more than 120 Palestinians dead, many of them civilians.