A number of patients at the facility in Kelso are said to have symptoms consistent with viral gastroenteritis.
Visitors are being "strongly discouraged" from coming to the hospital.
NHS Borders joint director of public health Dr Tim Patterson said anyone coming to the site should comply with any instruction from staff or on signs.
"Viral gastroenteritis is very infectious and spreads quickly between people," he said.
"This is why outbreaks happen in hospitals where a number of people are sharing facilities.
"However, it doesn't just occur in hospitals, and can start abruptly and spread quickly through communities."
He said patients, visitors and staff could all help minimise the impact of the outbreak by observing all hygiene instructions.
"This is vital to protect yourselves and your loved ones from catching this unpleasant virus, particularly as your friends or family members currently in hospital may be more vulnerable to the virus than usual," he said.
A Borders community hospital has been closed to admissions due to a stomach bug outbreak.