  We provide evidence of a superfluid-insulator transition (SIT) of magnons in
a quasi-one-dimensional quantum ferrimagnet with {\it isotropic} competing
antiferromagnetic spin interactions. This SIT occurs between two distinct
ferrimagnetic phases due to the frustration-induced closing of the gap to a
magnon excitation. It thus causes a coherent superposition of singlet and
triplet states at lattice unit cells and a power-law decay on the staggered
spin correlation function along the transverse direction to the spontaneous
magnetization. A hard-core boson map suggests that asymptotically close to the
SIT the magnons attain the Tonks-Girardeau limit. The quantized nature of the
condensed singlets is observed before a first-order transition to a singlet
magnetic spiral phase accompanied by critical antiferromagnetic ordering. In
the limit of strong frustration, the system undergoes a decoupling transition
to an isolated gapped two-leg ladder and a critical single linear chain.
