Israeli jets responded by striking targets in the Gaza Strip, the Israeli military said.
Defence Minister Avigdor Lieberman ordered the closure of both of Israel's border crossings with Gaza on Wednesday after a Palestinian rocket attack hit a southern city prompting retaliatory air strikes.
Lieberman ordered the closure of the Kerem Shalom goods crossing and the Erez crossing for people, and the reduction of the permitted fishing zone along the Gaza coast to three nautical miles, the defence ministry body responsible for Palestinian civil affairs, COGAT, said.
A medical official told Israel Radio that three people were taken to hospital after the rocket struck the house. Residents in the Gaza Strip said jets had targeted eight locations. The military said another rocket had been launched from Gaza, falling into the sea.
Health ministry officials in Gaza said three people were wounded in an Israeli air strike against an armed training camp in Rafah, in the south of the coastal strip. There were no reports of serious injuries in Israel.
Tensions along the Israel-Gaza border have been simmering for months amid weekly border protests and the launching by Palestinian militants of incendiary balloons and kites across the border fence.
Israeli leaders have warned that they are prepared to escalate military action on Gaza to curb attacks and protests. Israel and Hamas, which controls Gaza, fought a war in 2014.