Dr Lynn McCallum, Medical Director at NHS Borders
NHS Borders has also warned that changes may have to be introduced by GPs and other elements of primary care.
Hospital places are at more than 95 per cent capacity in the district with services also facing high staff absence rates caused by self-isolation rules as well as normal winter pressures.
The health board has also said it will ask relatives and carers of hospital patients who receive social care to help with tasks like washing and dressing their family members in a bid to free up staff time. It is also set to work on offers of interim arrangements for social care.
Dr Lynn McCallum, medical director of NHS Borders, described the decisions as "difficult" but said they were needed to keep services going.
She also said the high transmission rate of the Omicron variant meant case numbers were likely to continue to rise in the coming week.
Listen to our coronavirus podcast:
She added: "To make sure that we are able to continue vital services during this challenging time, it has been necessary to make a number of difficult decisions such as pausing routine surgery and moving to essential visiting. General practitioners and other primary care providers may also need to adjust the service they provide so that they."
The health board has said that "everything possible will be done so that all urgent, cancer and emergency surgeries will continue during this time" adding that a decision on routine operations being paused will be made "as soon as possible" but that it is "likely" this will happen.
Only essential visits are being allowed in hospital - such as birth partners, anyone accompanying a child or for people receiving end of life care - and anyone attending has been asked to take a lateral flow test before arrival. A detailed guide to essential visits can be found here.
This news comes in the same week that the NHS in Dumfries and Galloway announced it was moving to phase three of a "surge" plan, following a large number of Covid-19 cases being recorded there.
Dr McCallum also asked the public to recognise the pressures NHS staff are under.