Israel ordered border crossings closed after Palestinian militants fired a rocket on Sunday, which landed without causing casualties.
The Israeli defence minister decided on Monday night to allow a limited amount of fuel to be transferred into Gaza, after a request by Middle East Quartet peace envoy Tony Blair, Israeli officials said.
For all other purposes, the crossing would remain closed, they added.
The Gaza City plant provides about a quarter of Gaza's electricity, and more than half the electricity used by the city itself.
Most of the rest of the supply to the territory of 1.5 million people comes directly via power lines from Israel.
Palestinian engineers had been implementing a system of rolling blackouts to different areas of Gaza City to prevent the lines from Israel becoming overloaded and cutting out.
Without a grid system, they have no way to divert power to essential utilities such as hospitals or sewage treatment works. Aid agencies had warned of a serious threat to public health if the plant went offline.
Oxfam said Gaza's seven largest hospitals had stocks of diesel to supply generators for about a week, although one of the smaller ones - al-Quds hospital - had only 36 hours' supply.
The aid agency said that the water utility had no stocks of fuel for generators, which meant the sewage disposal system would break down as soon as mains electricity was cut.
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