High resolution transit spectroscopy has proven to be a reliable technique for the characterization of the chemical composition of exoplanet atmospheres. Taking advantage of the broad spectral coverage of the CARMENES spectrograph, we initiated a survey aimed at characterizing a broad range of planetary systems. Here, we report our observations of three transits of GJ 3470 b with CARMENES in search of He (2 3 S) absorption. On one of the nights, the He  I region was heavily contaminated by OH − telluric emission and, thus, it was not useful for our purposes. The remaining two nights had a very different signal-to-noise ratio (S/N) due to weather. They both indicate the presence of He (2 3 S) absorption in the transmission spectrum of GJ 3470 b, although a statistically valid detection can only be claimed for the night with higher S/N. For that night, we retrieved a 1.5 ± 0.3% absorption depth, translating into a R p ( λ )∕ R p = 1.15 ± 0.14 at this wavelength. Spectro-photometric light curves for this same night also indicate the presence of extra absorption during the planetary transit with a consistent absorption depth. The He (2 3 S) absorption is modeled in detail using a radiative transfer code, and the results of our modeling efforts are compared to the observations. We find that the mass-loss rate, Ṁ , is confined to a range of 3 × 10 10 g s −1 for T = 6000 K to 10 × 10 10 g s −1 for T = 9000 K. We discuss the physical mechanisms and implications of the He  I detection in GJ 3470 b and put it in context as compared to similar detections and non-detections in other Neptune-size planets. We also present improved stellar and planetary parameter determinations based on our visible and near-infrared observations.