The outage came two weeks after a massive blackout left more than 60 million people in the dark and raised questions about the nation's ability to host the 2014 World Cup and the 2016 Olympic Games in Rio.
Light SA, which supplies electricity to the city of 6 million, said only 12,000 clients were affected starting before dawn in the affluent Rio district of Leblon.
But lights were also out in Copacabana, Ipanema and Lagoa.
The four neighborhoods have more than 250,000 residents and are key tourist destinations.
The power company said the outage began when it cut off power to fix a problem with an underground cable. Electricity was restored to the beach areas by late afternoon, but Brazilian media reported that other neighborhoods in poor zones were still in the dark.
Tourists and shop workers sweated out the outage on the streets and on the beach as temperatures hit 95 degrees Fahrenheit (35 degrees Celsius) during the South American summer.
Sergio Perreira, owner of a beauty products shop near Ipanema beach, said he sent 25 employees home after losing nearly $15,000 in sales, plus electrical damage to his air conditioning units from power surges.
"I've never seen anything like this," said Perreira, 40. "If this keeps happening, how can this city host big events? You can't leave Ipanema without electricity."
The earlier blackout, on November 10, was caused by short circuits in a power substation that prompted the shutdown of three key transmission lines from the planet's second-largest hydroelectric dam, officials said.
Organizers of the 2016 Olympics are pitching host city Rio as a potential "power island" immune from blackouts, though experts have said the creation of such a safe energy haven would require large investments.
Brazil's electrical energy regulator gave Light two days to formally explain how the latest Rio blackouts happened, how long they lasted and what efforts are under way to make sure they don't happen again.