Chief fire officer Brian Sweeney told the BBC that the blaze was a "very, very serious and well-developed fire".
Strathclyde police said that they were called to the blaze just before 07:00 BST, but it is not yet known what caused it.
Chief Inspector Tom Aitken said that five elderly people had been trapped within the building for a short time as the fire service attempted to rescue the 89 residents and 15 staff inside at the time of the blaze.
He revealed that seven residents had been taken to nearby Hairmyres Hospital suffering from apparent smoke inhalation.
Mr Aitken confirmed that the fire has now been extinguished and that enquiries are ongoing to determine the cause of the blaze.
"Parts of the building have been unaffected by the fire and some of the residents have been taken back inside," he said.
The private care home, run by Southern Cross Healthcare, provides nursing, residential and respite care for the elderly and younger people with physical disabilities.
A spokeswoman for South Lanarkshire council said the local authority had the facilities in place to provide temporary accommodation for the home's residents if required.
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