Deputy Defense Minister Matan Vilnai told Israeli Army Radio the supply of gasoline to Gaza also will be "reduced slightly" to remind residents there are consequences for the rocket fire, IsraelNN.com reported.
On Tuesday, 22 rockets and 12 mortar shells were fired into Israel's western Negev region from the Gaza Strip. Several residents received minor injuries.
Monday, six rocket attacks were reported.
Vilnai said the power grid was set up in such a way that hospitals in the strip would not be affected by the power cuts.
The deputy said Defense Minister Ehud Barak was expected to approve the proposals in full at a Thursday defense meeting.