The sensitivity of low-loss perfluorinated polymer optical fiber (PF-POF) to gamma radiation is investigated for on-line radiation monitoring purposes. The radiation-induced attenuation (RIA) of a commercial PF-POF based on Cytop material is measured in the visible spectral region. The fiber RIA shows strong wavelength dependence with rapid increase towards the blue side of the spectrum. The wide range of radiation sensitivities is available via careful selection of appropriate monitoring wavelength. The accessible sensitivities span from 1.6 +/- 0.2 dBm-1/kGy measured at 750 nm to 18.3 +/- 0.7 dBm-1/kGy measured at 420 nm. The fairly high radiation sensitivity as well as its wide tunability makes the fiber a promising candidate for a broad range of applications.