The burgundy 1960s Gretsch Country Gentleman guitar belongs to Stuart Braithwaite, the frontman with Glasgow rock legends Mogwai.
It was stolen along with other equipment from the band's base in Glasgow city centre and was discovered missing last Saturday night.
In all, around £15,000 worth of gear was stolen. The vintage instrument was used by Stuart to record some of Mogwai's finest work, including Happy Songs for Happy People and Mr Beast.
The band are currently on tour in Australia.
Stephen Hines, an employee of the group's record label Rock Action Records, who discovered the break-in at the band's base, said: "This is Stuart's recording guitar. It doesn't even go on tour with him as it's very precious to him. I had to break the news to him."
Stuart said: "Everyone is gutted about this theft. We have been lucky that most of our equipment is currently on tour with us, meaning the theft could have been a lot worse."
Other items stolen include: two Orange guitar amp heads in black flight cases; an Orange bass amp head in a black flight case; a Marshall bass amp head in a silver flight case; a natural wood-coloured Fender acoustic guitar; and a black Fender 72 Telecaster Deluxe guitar.
It is the second blow to the band this year, after they lost the entire stock of their Earth Division EP in a fire at the PIAS record distribution centre during the London riots this summer.
The release had to be reprinted.
Anyone with information should call police on 0141 5323500.