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Nontrivial ground states appear in frustrated spin-1/2 chains involving ferromagnetic first-neighbor and antiferromagnetic second-neighbor exchange interactions, where spin-singlet short-range resonating valence bonds connect emergent spin-1 pairs with and without a spontaneously broken parity due to a vector spin chirality order. We report that the frustrated spin-1/2 ladder material Rb₂Cu₂Mo₃O₁₂, on which a ferroelectricity stabilized by a magnetic field has been reported, hosts effective spin-1 pairs forming a tetramer singlet ground state with the Haldane spin gap. Three lowest-energy spin excitations split from the spin-1 triplet by Dzyaloshinski-Moriya interactions are identified in inelastic neutron-scattering and electron spin resonance spectra. Overall experimentally measured magnetic properties are explained from numerical simulations on a frustrated spin-1/2 two-leg ladder model.