Searches for the lepton flavour violating decay $\tau^-\rightarrow \mu^-\mu^+\mu^-$ and the lepton flavour and baryon number violating decays $\tau^-\rightarrow \bar{p}\mu^+\mu^-$ and $\tau^-\rightarrow p\mu^-\mu^-$ have been carried out using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, taken by the LHCb experiment at $\sqrt{s} = 7$ TeV. No evidence has been found for any signal, and limits have been set at 90% confidence level on the branching fractions: $\cal B(\tau^-\rightarrow \mu^-\mu^+\mu^-) < 8.0 \times 10^{-8}$, $\cal B(\tau^-\rightarrow \bar{p}\mu^+\mu^-) < 3.3 \times 10^{-7}$ and $\cal B(\tau^-\rightarrow p\mu^-\mu^-) < 4.4 \times 10^{-7}$. The results for the $\tau^-\rightarrow \bar{p}\mu^+\mu^-$ and $\tau^-\rightarrow p\mu^-\mu^-$ decay modes represent the first direct experimental limits on these channels.