Fano resonance is a phenomenon in which a discrete state interferes with a continuum of states and has been observed in many areas of science. Here, we report on the prediction of a Fano resonance in ferroelectric relaxors, whose properties are poorly understood: an ab initio molecular dynamic scheme reveals such resonance between the bare optical phonon mode of the Zr sublattice (the discrete state) and the bare optical phonon mode of the Ti sublattice (the continuum of states) in disordered lead-free Ba(Zr,Ti)O3. The microscopic origins of the discrete state and continuum of states are discussed in the context of relaxor properties. Furthermore, our simulations suggest that the T* characteristic temperature of relaxor is related to a hardening of the vibrational frequencies associated with fluctuation of the Ti sublattice. Finally, a terahertz relaxation mode reflecting reorientations of Ti dipoles and showing a thermally activated behaviour is predicted, in agreement with previous experiments.