Engineered optical metamaterials present a unique platform for biosensing applications owing to their ability to confine light to nanoscale regions and to their spectral selectivity. Infrared plasmonic metamaterials are especially attractive because their resonant response can be accurately tuned to that of the vibrational modes of the target biomolecules. Here we introduce an infrared plasmonic surface based on a Fano-resonant asymmetric metamaterial exhibiting sharp resonances caused by the interference between subradiant and superradiant plasmonic resonances. Owing to the metamaterial's asymmetry, the frequency of the subradiant resonance can be precisely determined and matched to the molecule's vibrational fingerprints. A multipixel array of Fano-resonant asymmetric metamaterials is used as a platform for multispectral biosensing of nanometre-scale monolayers of recognition proteins and their surface orientation, as well as for detecting chemical binding of target antibodies to recognition proteins.