They are the Smoking Dog in the High Street and the Horse & Groom at Charlton.
They will be temporarily closed from today until further notice.
The company is also closing other pubs in Bristol, Bath, Cheltenham and Chew Magna following recent government announcements as the coronavirus crisis escalates.
Jonathan Lawson, chief executive officer of Liberation Group, which owns Butcombe Pubs & Inns, says: “We have made this incredibly difficult decision in order to consolidate our efforts, protect the business and save as many jobs as possible.
“Our team members are the lifeblood of our business and the responsible thing to do is to make sure we weather this storm and have opportunities and jobs for them to return to once this is all over.
“Our hope is to re-open these sites as soon as possible so we’ll be keeping a very close eye on developments and heeding advice when it’s given.
"We would like to thank all our colleagues and customers during this difficult time.”