The data, from Public Health Scotland, showed in the week ending January 11, more than 2,300 care home workers were unable to work due to the impact of the virus - an absence rate of 6.2%.
The week before, there was a 9.1% absence rate with 3,222 care home staff members off for Covid-related reasons.
The Scottish Labour Party said the latest figures show social care has been hit by the same staffing crisis currently affecting the NHS, with both sectors "buckling under pressure."
Earlier this week, the NHS reported its highest level of staff absences since April 2020.
PHS data showed that in the week ending January 11, 7,174 NHS staff reported as absent due to Covid, including more than 3,500 nurses and midwives and 150 medical and dental staff.
According to the Scottish Social Services Council's latest data on staff vacancies, one in three (36%) social care services had at least one vacancy at December 31 2020, which is more than three times the figure across all types of employers.
Service types reporting the highest levels of vacancies were housing support, (60%) care at home (59%), care homes for older people (55%) and care homes for adults (48%).
East Ayrshire (47% of services), Edinburgh (47% of services) and Renfrewshire (44% of services) had the highest proportion of services with vacancies of all local authority areas.
The most recent NHS workforce data showed there were 5,761 nursing and midwifery vacancies by September 2021 in Scotland.
Scottish Labour said the crisis is the result of "years of SNP underfunding and under-resourcing of the NHS and social care workforce at a time with record vacancies in both sectors".
Commenting on the figures, Scottish Labour deputy leader Jackie Baillie said: "The facts speak for themselves - staff absences have pushed our NHS and social care system to breaking point.
"The pandemic has shone a light on the years of mismanagement, underfunding and undervaluing that these vital workforces have suffered under the SNP.
"Years of SNP cuts are now leading to lives being put at risk across our health system and staff being worked to exhaustion.
"It's high time that the Cabinet Secretary woke up to the crisis unfolding in front of him and acted to get the situation under control."
Health Secretary Humza Yousaf said data shows infections and associated staff absences due to the coronavirus could peak by mid-January, and by treating more people at home with anti-virals, there will be more capacity in hospitals.
He pointed to the Scottish Government's £62m sum used to specifically enhance care at home services, adding: "All of this builds on work already underway as part of our £300 million investment in health and care services as part of winter preparations."
On high vacancy levels, Mr Yousaf said the government has introduced a new scheme where new staff joining the social care workforce will have entry costs paid by the Scottish Government until the end of March.
He added: "We will continue to work closely with our partners to identify all possible ways we can assist the sector to aid recruitment and retention within the workforce.”