The flat spectrum radio quasar 3C 279 is a known γ-ray variable source that has recently exhibited minute-scale variability at energies >100 MeV. One-zone leptonic models for blazar emission are severely constrained by the short time-scale variability that implies a very compact emission region at a distance of hundreds of Schwarzschild radii from the central black hole. Here, we investigate a hadronic scenario where GeV γ-rays are produced via proton synchrotron radiation. We also take into account the effects of the hadronically initiated electromagnetic cascades (EMC). For a γ-ray emitting region in rough equipartition between particles and kG magnetic fields, located within the broad-line region (BLR), the development of EMC redistributes the γ-ray luminosity to softer energy bands and eventually leads to broad-band spectra that differ from the observed ones. Suppression of EMC and energy equipartition are still possible, if the γ-ray emitting region is located beyond the BLR, is fast moving with Doppler factor (>70) and contains strong magnetic fields (>100 G). Yet, these conditions cannot be easily met in parsec-scale jets, thus disfavouring a proton synchrotron origin of the Fermi-LAT flare.