Mr Cameron spoke out after a study by the University of St Andrews indicated that death rates from Covid-19 could be between 50% and 80% higher in rural communities and remote small towns.
Currently the Western Isles has only reported six confirmed cases of the virus, with no new cases for the last 13 days.
The Highlands and Islands MSP told the Gazette: “The study makes for very sobering reading and suggests that remote communities, which tend to have older populations, are especially vulnerable.
“One of the authors of the report, Professor Kulu, has been quoted as saying: ‘The Welsh, Gaelic- and Cornish-speaking communities with relatively old populations are likely to experience heavy population losses if the virus spreads widely across the UK.’
“The Highlands and Islands have, at the moment, comparatively low infection rates and we want to keep it that way.
“This means that we will have to be very cautious before we suggest to visitors that they should consider venturing north. The last thing we want to see is a late spike in the infection rate in our part of the country.”