Plasmonic Fano metamaterials provide a unique platform for optical sensing applications due to their sharp spectral response and the ability to confine light to nanoscale regions that make them a strong prospect for refractive-index sensing. Higher order Fano resonance modes in noble metal plasmonic structures can further improve the sensitivity, but their applications are heavily limited by crosstalk between different modes due to the large damping rates and broadband spectral responses of the metal plasmon modes. Here, we create pure higher order Fano modes by designing asymmetric metamaterials comprised of a split-ring resonator and disk with a low-loss graphene plasmon. These higher order modes are highly sensitive to the nanoscale analyte (8 nm thick) both in refractive-index and in infrared vibrational fingerprint sensing, as demonstrated by the numerical calculation. The frequency sensitivity and figure-of-merit of the hexacontatetrapolar mode can reach 289 cm-1 per RIU and 29, respectively, and it can probe the weak infrared vibrational modes of the analyte with more than 400 times enhancement. The enhanced sensitivity and tunability of higher order Fano graphene metamaterials promise a high-performance nanoscale optical sensor.