The proton radiotherapy facility for the treatment of eye tumors is under development at the Institute of Nuclear Physics (IFJ) in Kraków. The optical line installed at the treatment room is applied to form and monitor the 60 MeV proton beam provided by the AIC-144 isochronous cyclotron. Typical proton dose rates measured at the isocentre varied between 0.01 and 0.5 Gy/s. The intensities of the secondary radiation field inside and around the treatment room have been measured with a stationary monitoring system. Four sets of radiation monitors provide the continuous monitoring of gamma and neutron radiation during the operation of the facility. Monte Carlo calculations have been performed for understanding the structure of the radiation field inside the treatment room. Typical ambient dose equivalent rates inside the treatment room vary between 100 and 800 μSv/h for neutrons and between 10 and 130 μSv/h for gamma rays. The maximum values were found to be 2.5 mSv/h and 0.3 mSv/h respectively. The ambient dose equivalent rates outside the therapy room were not higher than 2.5 μSv/h for neutrons and 0.35 μSv/h for gamma rays. The end of the beam line, the optical line and the beam scattering system are main sources of the secondary radiation. Optimisation and shielding of these elements will reduce the patient and facility personnel exposure to the secondary radiation.