Douglas Harper's Etymology Dictionary
1570s, from barber + shop (n.). Earlier in same sense was barbery (c.1500). Barber-shop in reference to close harmony male vocal quartets, it is attested from 1910; the custom of barber's keeping a musical instrument in their shops so waiting customers could entertain themselves is an old one, but the musical product had a low reputation and barber's music (c.1660) was "wretched, poorly performed music."
Wiktionary
n. (attributive of barber shop English)
Usage examples of "barber-shop".
An hour later Willy and Samuel climbed back into their jalopy, which someone, they never knew who, had washed and polished while they were in the barber-shop.
Turning down Main Street at the City Hotel corner, on the way to my office, I had to pass the barber-shop of Harpin Cust, in front of which I found myself impelled to stop.