The boy was shot in the chest late on Monday and died in a hospital in San Felix, 650 kilometres southeast of the capital of Caracas, the Bolivar state police said in a statement, without offering further details.
Protesters threw Molotov cocktails at a police post, partially burning it, the statement added.
A Reuters witness late on Monday confirmed seeing a protest in the area over the lack of electrical power.
Residents of the oil-rich nation have increasingly objected to the steady decay of basic services including power and water, part of an economic crisis that has also created shortages of food and medicine, and driving millions to flee the country.
The Information Ministry did not immediately reply to a request for comment.