We present evidence for anomalous microwave emission (AME) in the Pleiades reflection nebula, using data from the seven-year release of the Wilkinson Microwave Anisotropy Probe and from the COSMOSOMAS (Cosmological Structures on Medium Angular Scales) experiment. The flux integrated in a 1° radius around R.A. = 56fdg24, decl. = 23fdg78 (J2000) is 2.15 ± 0.12 Jy at 22.8 GHz, where AME is dominant. COSMOSOMAS data show no significant emission, but allow one to set upper limits of 0.94 and 1.58 Jy (99.7% confidence level), respectively, at 10.9 and 14.7 GHz, which are crucial to pin down the AME spectrum at these frequencies, and to discard any other emission mechanisms which could have an important contribution to the signal detected at 22.8 GHz. We estimate the expected level of free-free emission from an extinction-corrected Hα template, while the thermal dust emission is characterized from infrared DIRBE data and extrapolated to microwave frequencies. When we deduct the contribution from these two components at 22.8 GHz, the residual flux, associated with AME, is 2.12 ± 0.12 Jy (17.7σ). The spectral energy distribution from 10 to 60 GHz can be accurately fitted with a model of electric dipole emission from small spinning dust grains distributed in two separated phases of molecular and atomic gas, respectively. The dust emissivity, calculated by correlating the 22.8 GHz data with 100 μm data, is found to be 4.36 ± 0.17 μK (MJy sr-1)-1, a value considerably lower than in typical AME clouds, which present emissivities of ~20 μK (MJy sr-1)-1, although higher than the 0.2 μK (MJy sr-1)-1 of the translucent cloud LDN 1780, where AME has recently been claimed. The physical properties of the Pleiades nebula, in particular its low extinction A V ~ 0.4, indicate that this is indeed a much less opaque object than those where AME has usually been studied. This fact, together with the broad knowledge of the stellar content of this region, provides an excellent testbed for AME characterization in physical conditions different from those generally explored up to now.