Recently, the YbOH molecule has been suggested as a candidate to search for the electron electric dipole moment (eEDM), which violates spatial parity (P) and time-reversal (T) symmetries [I. Kozyryev and N. R. Hutzler, Phys. Rev. Lett. 119, 133002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.133002]. In the present paper, we show that the same system can be used to measure coupling constants of the interaction of electrons and nucleus mediated by axionlike particles. The electron-nucleus interaction produced by the axion exchange can contribute to a T,P-violating EDM of the whole molecular system. We express the corresponding T,P-violating energy shift produced by this effect in terms of the axion mass and product of the axion-nucleus and axion-electron coupling constants.