  We investigate the behavior of an $N$-component quantum rotor coupled to a
bosonic dissipative bath having a sub-Ohmic spectral density $J(\omega) \propto
\omega^s$ with $s<1$. With increasing dissipation strength, this system
undergoes a quantum phase transition from a delocalized phase to a localized
phase. We determine the exact critical behavior of this transition in the
large-$N$ limit. For $1>s>1/2$, we find nontrivial critical behavior
corresponding to an interacting renormalization group fixed point while we find
mean-field behavior for $s<1/2$. The results agree with those of the
corresponding long-range interacting classical model. The quantum-to-classical
mapping is therefore valid for the sub-Ohmic rotor model.
