Higher order Fano resonance metamaterials provide a desirable platform for biosensing applications. In this work we exhibit higher order Fano modes by designing an elliptical metallic ring. The simulation results show that for Fano resonant metamaterials, the higher order modes lead to improved sensitivity to refractive index change and larger frequency shifts. Numerically, the sensitivity of dip A (quadrupole mode) is 112 GHz/RIU, whereas the sensitivity of dip B (octupole mode) is 234 GHz/RIU, over 2 times that of dip A. According to our experimental results, the Fano resonant frequencies of dip A and dip B exhibit redshift as the concentration of the anti-cancer drug methotrexate decreases from 120 to 90 μM, with the cell analyte concentration of A549 cells at 5×105 cell/ml. For dip A (quadrupole mode), there is a frequency shift of 0.84 GHz for drug concentration of 120 μM and a frequency shift of 22 GHz for a 90 μM drug-treated sample. For dip B (octupole mode), there is a frequency shift of 6.767 GHz for the drug concentration of 120 μM treated sample and a frequency shift of 51.815 GHz for the drug concentration of 90 μM treated sample. Furthermore, the frequency shift of dip A is always smaller than that of dip B for both 90 μM and 120 μM drug concentrations. Such phenomena indicate that dip B is much more sensitive than dip A. The enhanced sensitivity of higher order Fano metamaterials makes it possible to realize high-performance terahertz sensing for biomedical applications.