Using the tight binding description of the electronic structure of graphene and a time-dependent quantum approach, we address the vibrational excitation of molecules in the near field of a graphene nanoantenna. The possibility of tuning the graphene plasmon frequency by electrostatic doping allows an efficient resonant excitation of the infrared (IR)-active vibrational modes via the coupling between the molecular dipole and plasmon near field. We show that for the carbon monoxide CO molecules placed in the gap of a dimer antenna formed by the 20 nm size graphene patches, an excitation of the υ=1←0 transition leads to a distinct molecular signature in the IR absorption spectrum of the system. A very small number of molecules down to a single molecule placed in the antenna gap can thus be detected. Along with IR-active vibrations, the inhomogeneity of the plasmonic near field allows vibrational excitation of IR-inactive molecules via molecular quadrupole. The resonant excitation of the N2 molecule vibration is thus observed in the calculated absorption spectra, albeit the molecule signature is essentially smaller than for the CO molecule. Obtained with molecules described on the ab initio quantum chemistry level, our results provide quantitative insights into the performance of graphene nanoflakes and their dimers for molecular sensing.