NHS Borders said urgent and cancer procedures will still go ahead.
The health board had already cancelled all routine planned operations at Borders General Hospital until the end of December.
It is now preparing for a further increase in demand as the number of confirmed Covid cases in the Borders continues to increase, and has taken the "very difficult decision" to cancel routine planned operations.
Ralph Roberts, chief executive at NHS Borders, said: "Taking this decision is not easy but it is necessary to make sure that we are able to continue vital services during this challenging time. We continue to see a rise in the number of confirmed cases of Covid-19 in the Borders and we must plan our services accordingly.
"I would like to apologise to those that this decision affects and I fully appreciate and understand how disappointing this must be. However I hope you will understand that patient and staff safety is our top priority, including providing the highest quality of care and support."Winter places a great deal of pressure on health and care services every year, and that is without including the impact of this deadly virus.
"The actions we all take now will have an impact in the coming months so please follow the rules. These rules are really important if we are to keep each other safe and allow time for the Covid vaccination programme to take place over the coming months."