NHS Highland services including primary care and community, mental health and acute services are seeing “unprecedented” levels of demand, the health board said.
Staff numbers have also been reduced by increasing numbers self-isolating after contact with a positive Covid case.
It comes as NHS Tayside opened an extra Covid-19 ward in Ninewells hospital to cope with increasing Covid cases.
Dundee which is within the health board area, currently has the highest rate of Covid in the country.
Dr Pamela Johnston, operational medical director at NHS Tayside said, “As the number of new cases of Covid-19 across Tayside continues to rise, we are seeing an increase in demand on our services.
“We currently have 20 patients in hospital requiring care for Covid and unfortunately, we expect this number to increase over the next few weeks.
“As part of our plans, we are opening an additional ward in Ninewells Hospital to care for these patients.
“Our GPs at the Covid Assessment Centre are also very busy, seeing five times as many people as last month who are feeling very unwell with the virus and coming for assessment and a proportion of these do require hospital admission.
“What is different for the hospital this time is that there are more emergency surgical and medical patient admissions than at the start of the year and than during the previous waves.
" All of our health and care services are under increasing strain from this demand. We also have a number of staff self-isolating, which is adding to the challenge.”
Dundee’s case rate is currently 765 per 100,000 people, while the rate in Scotland is 359. In the Highland council area it is 189.
A spokesperson for NHS Highland said: "All steps are being taken to manage patients as safely as possible within the Highland system.
"Patients presenting at emergency departments are being given information on NHS 24 as well as suitable alternatives for care.
"To ensure you have the fastest access to the treatment you need, anyone with a non-life-threatening condition who would usually go to A&E should call NHS 24 on 11 first, day or night, to be directed to the right NHS service.”