NHS Borders chief executive Ralph Roberts said the board was dealing with a “very challenging situation” as he confirmed they were grappling with high rates of Covid-19 related staff absence.
It was announced on Monday that Borders General Hospital, near Melrose, was at capacity, with all beds fully occupied.
The decision to cancel routine operations follows a widespread surge in Covid cases, with one in 18 people in Scotland estimated to have the infection in the week ending June 24.
Ward nine at the BGH and Hay Lodge Hospital in Peebles remain closed as a result of Covid-19 outbreaks.
In a statement, Mr Roberts said: “In order to alleviate these pressures, reluctantly all planned routine operations have been cancelled this week.
"Affected patients are being contacted directly. Everything possible will be done so that urgent cancer and emergency surgery continues during this time. We are truly sorry to the patients affected by these decisions.”
NHS Borders was unable to confirm how many of the beds at Borders General were being taken up by Covid cases.
Mr Roberts said the health board’s “surge capacity plans” were in place and that staff were doing everything they could to free up beds.
He urged members of the the public to call NHS 24 before attending the health board’s emergency department, which he described as “exceptionally busy”.
Professor Hugh Pennington, from the University of Aberdeen, said last week it was not clear why case rates were higher in Scotland than elsewhere in the UK.
The esteemed microbiologist has suggested a strengthened publicity campaign is needed to encourage people to wear masks indoors to help limit the spread of Covid.