“Prince Joachim's situation is still stable. He is doing well in the circumstances,” the Ritzau news agency quoted the palace as saying after the prince's surgery on Friday at Toulouse University Hospital.
Joachim, 51 and sixth in line to the Danish throne, was holidaying with his family at Cayx, a chateau the royal family owns in southwestern France, when he was taken ill.
The palace added that Joachim, contrary to earlier Danish media reports saying he had been taken by helicopter, was driven by ambulance to the hospital, 130 kilometres (90 miles) away.
“It is too early to say right now,” palace spokeswoman Lene Balleby said with regard to how long the prince would remain hospitalised.
He became ill shortly after an interview for a local paper with French reporters, who described a “relaxed” encounter.
Joachim, whose late father, Prince Consort Henrik was of French origin, is the younger brother of Crown Prince Frederik, who is in line to succeed their 80-year-old mother.
Twice-married Joachim, an army colonel of the reserve, is a father of four — two sons Nikolai, 20, and Felix, 18 from his first marriage and two with second wife Princess Marie — Henrik, 11), and Athena, eight.
Joachim is due to begin serving as military attache at the Danish embassy in Paris in September.