The rocket struck the home in Kibbutz Zikkim, according to the Israel Defense Forces. The child's injuries are not life-threatening.
Last week, Israeli Defense Minister Ehud Barak announced he was seeking renewal of a declaration of a "special situation" in Israeli communities near the Gaza border that are frequently bombarded with rockets from Palestinian militants in Gaza.
The declaration allows the Israeli military a greater amount of control in those communities, but needs to be approved by the cabinet and the Knesset.
According to the Israeli military, over 3,600 rockets and mortars have been fired from Gaza into Israel since Israel pulled out its troops and settlements from Gaza in 2005.
The military said the number of rocket attacks has more than doubled since Hamas seized control of Gaza in June.
The situation threatens to overshadow the burgeoning Israeli-Palestinian peace process.
