The rocket hit the Eshkol region without causing any casualties or damage, officials said.
The attack came just over a week after the Palestinians formed a unity government for both Gaza and the West Bank, as part of efforts to end years of division.
From 2007, when Hamas drove Abbas's forces from Gaza, the territory was ruled by Islamist movement Hamas, which Israeli routinely blamed for all attacks on the Jewish state.
Now, a spokesman for Prime Minister Benjamin Netanyahu said Abbas, who heads the unity government, is responsible for rocket fire from Gaza.
Another Netanyahu spokesmen released a statement demanding that Abbas disarm "terrorist" organisations in Gaza.
"Abbas claims that the new Palestinian government honours all previous commitments. So why has he not disarmed the terrorist organisations in Gaza as he is obligated to do," Mark Regev asked.
The new government of independent technocrats agreed on between Abbas's Fatah party and Hamas, has said it will respect past agreements with Israel, and given assurances that it will recognise Israel and renounce violence.
Some 140 projectiles fired by militants in the Gaza Strip have hit southern Israel since the start of 2014, the military says.
On June 1, two rockets from Gaza hit Israel, prompting retaliatory raids by the Israeli air force.
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