We show that the wandering of transition frequencies in colloidal quantum dots does not follow the statistics expected for ordinary diffusive processes. The trajectory of this anomalous spectral diffusion is characterized by a sqrt[t] dependence of the squared deviation. The behavior is reproduced when the electronic states of quantum dots are assumed to interact with environments such as, for example, an ensemble of two-level systems, where the correlation times are distributed according to a power law similar to the one generally attributed to the dot's luminescence intermittency.