During the last few years, exact solutions describing black holes bound to a 2-brane in a four-dimensional anti-de Sitter bulk have been constructed. In situations where there is a negative cosmological constant on the brane for large masses, these solutions are exactly the rotating Banados-Teitleboim- Zanelli (BTZ) black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick-wall model. We explicitly show that the Bekenstein-Hawking 'area' law is satisfied both on the brane and in the bulk. © 2007 IOP Publishing Ltd.