The Category B listed Poosie Nansie's Inn in the East Ayrshire town of Mauchline was a favourite haunt of the ploughman-poet.
Scotland's national poet lived and worked in Mauchline between 1784 and 1788.
The house he shared with Jean Armour is now a museum in nearby Castle Street.
Twenty-five firefighters from Mauchline, Kilmarnock and Cumnock attended Poosie Nansie's shortly after noon on Sunday.
They were supported by a Heavy Rescue Vehicle from Easterhouse and a Major Incident Unit from Clydebank. No-one was injured.
Firefighters were "shoring" up the damaged end of the building to secure it, in order to prevent any further collapse. The area was cordoned off.
Mossgiel Farm in Mauchline was home to Burns when he was ploughman-poet and wrote many of his best loved works.
Firefighters have been working to secure a historic building with links to Robert Burns after a partial wall collapse.