Free electrons or holes can mediate the nonradiative recombination of excitons in carbon nanotubes. Kinematic constraints arising from the quasi-one-dimensional nature of excitons and charge carriers lead to a thermal activation barrier for the process. However, a model calculation suggests that the rate of recombination mediated by a free electron is the same order of magnitude as that of two-exciton recombination. Small amounts of doping may contribute to the short exciton lifetimes and low quantum yields observed in carbon nanotubes.