Large distance implementation of quantum communication technologies requires coherent control of single photons in optical fiber networks. Here we demonstrate the phenomenon of coherent perfect absorption of single photons in a fully fiberized ultrathin plasmonic metamaterial fabricated at the end facet of an optical fiber. Continuous control of single-photon absorption probability is achieved by driving the network between the regimes of coherent total absorption and coherent total transmission. To circumvent phase fluctuations inherent to optical fiber networks, we implemented a reference-based postselection technique which yielded interference fringe visibility comparable to that of free space experiments. Coherent absorption of quantum light in fiber environment provides new opportunities for dissipative single-photon switching, filtering, and measurement, as well as for manipulation of entangled, weak coherent, and NOON states in optical fiber networks.