IRAS 01005+7910 is a carbon-rich protoplanetary nebula with a recently reported detection of mid-IR vibrational transitions of the fullerene C60 by Zhang and Kwok. We present new high spectral resolution (R ~ 57, 000) observations of this object obtained at the 3.6 m Telescopio Nazionale Galileo, showing the presence of two absorption bands at 9577 and 9632 Å which are consistent with laboratory measurements of the C_{60}^+ cation. If these two bands were produced by C_{60}^+ in the material surrounding the central post-asymptotic giant branch star, we estimate that ~1% of carbon could be trapped in this ionized form of fullerenes which would be more abundant than the neutral species in this protoplanetary nebulae. The central star with an effective temperature of T >= 20, 000 K can provide the ionizing photons required. These observations bring further evidence for the presence of fullerenes in protoplanetary nebulae and suggest that a significant production takes place in this late stage of stellar evolution. Mid-IR bands of C_{60}^+ could be present in the 7-20 μm spectrum of IRAS 01005+7910 and are also likely to be detected in the spectra of planetary nebulae. High-resolution spectroscopy will be required for a reliable determination of the excitation temperatures and the relative abundance of neutral and ionized fullerenes in these objects.