There probably was no merchandise sold for Bach concerts when he was still alive, and I suspect Elvis or the Beatles also had no such thing, but by the 1980s they were abundant. So do we know who were the first to do this?
Can I tack on a question? The answers below say shirts started being sold in the late 50s. Did popular acts sell "swag" at their shows before that? (e.g., if you went to a Duke Ellington show in the 30s or a popular act in the 1890s, would there be braded items you could buy?)
"Many T-shirt collectors today try to accumulate old rock concert T’s. While some of the most famous and collected rock T-shirts come from world-famous groups like The Rolling Stones and Led Zeppelin, concert T-shirts actually originated earlier: with The King himself.
One of Elvis’ fan clubs printed the first rock concert T-shirt in the late 1950s. Despite Presley’s popularity, rock concert or music personality T-shirts did not become fashionable until the late 1960s, when impresario Bill Graham promoted West Coast bands like the Grateful Dead and Jefferson Airplane. Some of the earliest and most collectible vintage T-shirts advertise those groups and others associated with the San Francisco music scene. Vintage tie-dyed shirts from this era are especially prized." Source- http://www.collectorsweekly.com/mens-clothing/t-shirts