The decision to end the life of 6-year-old Dolly was made after a veterinary examination confirmed the lung disease, a statement from the institute said.
Dolly was born in 1996, and she created an international sensation when the Scottish research institute announced its achievement on Feb. 23, 1997.
In 1999, scientists noticed that the cells in Dolly's body - cloned from a 6-year-old sheep - had started to show signs of wear more typical of an older animal.
Some geneticists said the finding provided evidence that researchers could not manufacture copies of animals without the original genetic blueprint eventually wearing out.
Many attempts to clone animals have ended in failure. Deformed fetuses have died in the womb with oversized organs, while others were born dead. Still others died days after being born, some twice as large as they should have been.
Dr. Harry Griffin of the Roslin Institute, near Edinburgh, said Friday that sheep can live to 11 or 12 years and lung infections are common in older sheep, particularly those housed inside.
"A full post-mortem is being conducted and we will report any significant findings," Griffin said.
Last year Dolly's creators announced she had developed arthritis at the relatively early age of 5 1/2 years, stirring debate over whether cloning procedures might be flawed.
Prof. Ian Wilmut, the leader of the team that created Dolly, said in January 2002 that apart from the arthritis, Dolly remained a healthy animal who has given birth to six lambs.
He also said Dolly was responding well to a treatment with anti-inflammatory drugs and that her condition will be closely monitored.
By Jane Wardell