The hospital in the town of Pointe-a-Pitre gave no further details on Hallyday, 69, but said he would be transferred from the Caribbean island, a French overseas territory, to a facility in nearby Martinique for tests.
"His condition is judged to be stable," the hospital's director said in a statement, later adding that Hallyday would not need to be kept in hospital.
French media initially reported that Hallyday was suffering from tachycardia, an abnormally fast heartbeat, but his producer issued a statement denying reports of heart trouble and saying that Hallyday had been hospitalized as a precautionary measure.
"If I had the slightest worry I would not be sitting in Paris behind my desk -- I would be on the first plane to go and see him," the producer, Gilbert Coullier, told BFM television.
Hallyday, one of France's most successful musicians with a huge following in his home country, fell ill while taking a break in the island of St Barts from a marathon concert tour with dozens of dates and stops scheduled in London, New York, Tel Aviv and Moscow.
A self-styled Gallic Elvis with a gravelly voice and a cowboy swagger, Hallyday's fans include former President Nicolas Sarkozy, who set up a fan club to him at the National Assembly and is said to know his song lyrics by heart.
Brushing off suggestions that Hallyday's life may be in danger, Coullier said there were no plans to cancel the tour or reschedule the start of recording for a new album. "I am sure he will return to good health in the coming hours," he said.
Coullier later told RTL radio that Hallyday was keen to leave the hospital. "He's totally conscious, he's talking, he is as good as you can be. It's bronchitis which was poorly treated. He's out of breath and has trouble breathing, and he's there to fix that up but it's no more serious than that."
It was not the first health scare for the hard-living rocker who had to be put into an induced coma in late 2009 after complications during a hernia operation in Los Angeles.
His son, David Hallyday, suggested in a Twitter message that signs of his father's health were encouraging, saying: "The news is very good, which is very reassuring to us."
(Reporting by Dominique Chomereau-Lamotte and Gerard Bon; Writing by Nick Vinocur; Editing by Catherine Bremer and Bob Tourtellotte)
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