NHS Borders said a number of patients were suffering from "gastrointestinal symptoms".
Ward 12 has been shut as well as a bay in Ward 16 and a bay in the hospital's stroke unit.
Visitors to Ward 12 have been "strongly discouraged", with relatives and carers asked to "carefully consider" visiting.
A sickness bug outbreak has prompted the closure of one ward and two bays at the Borders General Hospital to new admissions.