Ohi nuclear plant's reactor No 3, in the western Fukui Prefecture, returned to operation on Sunday evening despite a deep division in public opinion.
Many citizens are against a return to nuclear power because of safety fears after the Fukushima accident in March last year.
Crowds of tens of thousands of people had gathered on Friday evening around Noda's official residence, chanting, "Saikado hantai," or "No to nuclear restarts."
Protests drawing such numbers are extremely rare in Japan, often known for orderly conformity.
A demonstration in Tokyo protesting against the restart and demanding Noda resign was planned in a major park on Sunday.
Although initially ignored by mainstream local media, demonstrations across the country have grown as word spread through social media.
Protests have included Japanese celebrities, such as Nobel Prize-winning writer Kenzaburo Oe and Ryuichi Sakamoto, who composed the score for the movie The Last Emperor .
All 50 of Japan's working reactors were gradually turned off in the wake of last year's massive earthquake and tsunami, which sent the Fukushima Dai-ichi plant into multiple meltdowns, setting off the worst nuclear disaster since Chernobyl.
But worries about a power crunch over the hot summer months have been growing.
Oil imports are soaring and officials have warned about blackouts in some regions.
The government has been carrying out new safety tests on nuclear plants, and says Ohi No 3 and No 4 are safe to restart.
Protesters like Taisuke Kohno, a 41-year-old musician among the 200 people trying to blockade the Ohi plant, are not so sure. Kohno said protesters were facing off against riot police and planned to stay there day and night.
"It's a lie that nuclear energy is clean," he said. "After experiencing the nuclear bombing of Hiroshima and Nagasaki, how can Japan possibly want nuclear power?"
Kansai Electric Power Co, the utility that operates Ohi in central Japan, was not immediately available for comment Sunday.
It said on its website that a nuclear reaction restarted Sunday afternoon at the No 3 reactor, a key step for it to begin producing electricity.
Fukushima Dai-ichi, in northeastern Japan, went into meltdowns and exploded after the March 11 tsunami destroyed backup generators to keep the reactor cores cool.
In the latest problem at the crippled plant, Tokyo Electric Power Co, its operator, said the cooling system for the spent nuclear fuel pool at reactor No 4 broke down on Saturday, and a temporary system was set up Sunday.
The cooling system had to be restored within 70 hours, or temperatures would have started to rise, spewing radiation.