We measure two-photon absorption (2PA) spectra of wild-type green fluorescent protein, cyan fluorescent protein, and monomeric red fluorescent protein in absolute cross section values in a wide spectral range (lambda2PA = 550 - 1300 nm), and find, for the first time to our knowledge, a new S0 --> Sn 2PA transition in all three proteins in the short-wavelength region. This transition is strongly resonantly enhanced, showing 2PA cross section values of approximately 20-160 GM, which are at least 2-4 times higher than those measured in the lowest energy (S0 --> S1) transition of corresponding proteins. We also show that the change of permanent dipole moment upon S0 --> S1 excitation (|Deltamu10|) can be deduced from 2PA cross section, providing a new tool for fast evaluation of |Deltamu10| in physiological conditions.