The rocket hit Sderot, part of which lies less than a kilometre northeast of the Gaza Strip, run by Islamist movement Hamas, the Israeli military said.
The area was closed off and bomb disposal teams were working at the site, police spokesman Micky Rosenfeld said.
A small Salafist group -- followers of an ultra-conservative brand of Sunni Islam who oppose Hamas -- claimed responsibility for the attack.
"Thanks to God, the so-called Sderot settlement was targeted by a homemade rocket," the Ahfad al-Sahaba group said in a statement.
Shortly afterwards, Hamas security sources said Israeli tank fire struck a post run by its military wing, the Ezzedine Al-Qassam Brigades, east of Beit Hanoun near the border with Israel.
Three air strikes also targeted other bases in the Khan Yunis area in the south of the enclave, the sources said, while two others hit Hamas posts near Gaza City, an AFP journalist reported.
The Israeli military did not immediately comment.
The Israeli army and Palestinian militants in Gaza have fought three wars since 2008 and there are frequent flare-ups along the border.
In August, it carried out dozens of retaliatory strikes after a rocket hit Sderot, a far larger response than usual.
Israeli media reported that attack was the first time downtown Sderot had been struck by a rocket from Gaza since the last war in 2014.
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