Although several animals - sheep, cattle, goats and mice - have been cloned, many die before birth or are born with severe abnormalities.
Scientists believe the disease could have been caused by the cloning process. BBC News Online looks at the implications for the future of cloning.
What is the matter with Dolly?
She has developed arthritis in the hip and knee of her left hind leg at an unusually young age.
According to one of the scientists who produced Dolly, it could be due to some sort of problem with the cloning process itself.
Although several animals - sheep, cattle, goats and mice - have been cloned, many die before birth or are born with severe abnormalities.
This had led to concern that even those animal clones which appear healthy may in fact have underlying genetic abnormalities.
Dolly was born in 1996 and revealed to the world in 1997. Under normal circumstances, sheep can live for 10-16 years - so she is still relatively young.
Dolly was created using DNA taken from an adult cell, in this case the udder of a ewe. The fact that Dolly's genetic material came from a six-year-old sheep may mean that she ages quicker than normal.
Until now, she has shown no signs of ill health and has given birth to six healthy lambs.
Do sheep normally get arthritis at Dolly's age?
According to Dr Dai Grove-White of the Faculty of Veterinary Science at Liverpool University, UK, arthritis is not a particularly common disease in sheep and is not well recognised.
But he said it was very difficult to make a judgement based on just one sheep.
"Conceivably [arthritis] could be due to the cloning but equally it could not be," he told BBC News Online. "For all we know, she may have damaged her leg jumping over a gate and developed arthritis."
He added: "The development of arthritis in Dolly should not be used as a reason to hinder cloning but her arthritis should be investigated fully as to cause."
Dr Colin Macaldowie of the Sheep Veterinary Society at the Moredun Research Institute, Midlothian, Scotland, said Dolly's condition needed to be studied carefully given her background.
But he said it was not a reason to stop animal cloning experiments.
He told BBC News Online: "There are tremendous advances that can be gained from this technology and it would be unfortunate to take a knee-jerk reaction. But we need to proceed with caution."
He said there were a number of treatments for a sheep with arthritis, including anti-inflammatory drugs and restrictive exercise.
What are the implications for animal cloning experiments?
Professor Ian Wilmut, who led the team that created Dolly, has called for more transparency from researchers working in the field.
He believes other experts may have long-term data on cloning abnormalities that they are not revealing because of the bad publicity it might generate.
Most cloning research is carried out by companies rather than universities.
Any hints that work is not progressing smoothly can damage the finances of those companies.
Professor Wilmut believes scientists in the cloning field need to be more open and to share their data with each other.
This may answer the question of whether Dolly developing arthritis is a coincidence or a serious concern.