A thick column of black smoke rose from the facility, which supplies the territory with two-thirds of its energy needs, and the fuel containers were in flames.
"The power plant is finished," said its director, Mohammed al-Sharif.
He said the local fire brigade was not equipped to extinguish the blaze.
An Israeli military spokeswoman had no immediate comment and said she was checking the report.
The plant had already been hit last week and was working at a reduced capacity of about 20 percent, allowing only a few hours of electricity a day for Gaza's residents.
Israel launched a military offensive in Gaza on July 8, saying it wanted to halt rocket attacks by the dominant Hamas movement and other armed groups. Ten days later, it sent in ground forces with the declared aim of destroying Hamas tunnels that criss-cross the border area.
Though international pressure has been mounting to end the fighting, there is no end in sight to the 22-day conflict in which 1,116 Palestinians, many of them civilians, and 53 Israeli soldiers and three civilians have been killed.