Around 80 construction jobs are believed to be under threat at its Creetown fabrication site in Dumfries and Galloway, and at its base in Killoch, near Cumnock in Ayrshire.
Employees have been issued with official 30-day consultation notices.
Barr blamed difficult trading conditions with the Scottish construction industry facing “unprecedented economic challenges”.
A spokesman told the BBC said: “At a global level, manufacturing and fabrication have been especially hard hit over the past two years and this has resulted in the unfortunate but necessary requirement for us to conduct an operational review of the entire Solway Structural Steel business.”
He added: “We have done everything possible to avoid this regrettable situation and will be consulting extensively with Solway Steel personnel and their representatives in the coming weeks.”