Home Farm care home in Portree, the island's main town, has a "small number of confirmed cases" of the potentially deadly virus with staff members self-isolating.
A spokesman for HC-One, the firm which operates the home, confirmed there has been no deaths linked to coronavirus and said families of those who have tested positive have been notified.
The island has 10,000 residents and a community group warned that although other parts of the UK had seen a peak, locally it was just starting.
A spokesman for NHS Highland said: "There is an independent care home in Portree, Skye with a Covid-19 outbreak.
"There is substantial testing underway to fully understand the extent of infection.
"The care home is being supported through the health protection team within public health, local health and social care teams, primary care as well as the adult social care functions within NHS Highland.
"All assistance will be made available to the care home in order to contain and manage the situation."
A HC-One spokesman said: "We have a comprehensive coronavirus contingency plan in place, which was created by our clinical director and reflects the latest government guidance.
"We are working closely with our local health and care partners, and we have all the medical equipment, PPE, and supplies we need to protect residents and colleagues.
"While a small number of colleagues are self-isolating, we continue to have the team needed to support our residents.
"We are also receiving additional support from our regional team."
A statement from Skye Community Response said: "It was expected that our community would begin to see cases.
"It was a question of when, not if this would happen.
"Be assured that your fantastic NHS and health care services were prepared for this and are giving the best possible care to those impacted.
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