The nuclear reactor was taken out of service at 7 p.m. Sunday. Plant spokesman Larry Smith estimated it would take 13 hours to cool down enough for workers to enter the area and make repairs.
Smith said the leak of about 60 drops a minute was spotted earlier Sunday during routine surveillance. It was coming from a 2-foot-wide pipe that was part of the circulation system involving the reactor, he said. The water was being collected by a sump pump and cycled back through the system, he said.
The cause of the leak was not immediately known. The Nuclear Regulatory Commission said the public was not in any danger.
It was the second shutdown within an hour at a plant owned by New Orleans-based Entergy Corp.
A transformer exploded at a nuclear power plant north of New York City, forcing an emergency shutdown of one of its reactors. No one was injured and no radioactive materials leaked.
Entergy announced last week that it would put the Vermont Yankee plant up for sale.