We analyse the data from the Fermi-Large Area Telescope in order to search for a ring-like γ-ray structure around the Coma cluster. The ring-like structure has recently been suggested to be detected with VERITAS at energies higher than 220 GeV and could possibly be associated with an accretion shock. Our analysis of the Fermi data is performed at energies >100 MeV and we find no detection of this structure in the Fermi data. We derive the 95 per cent upper limit on the flux from the region covering the proposed ring-like structure. The derived upper limit on the flux at >100 MeV cannot be incorporated with the detection of an accretion shock wave around Coma at the significance of 4.5σ by VERITAS at very high energies, if the production mechanism of the γ-ray emission generates a photon spectrum with a power index of 2 in the broad energy band. The model of γ-ray emission induced by ultrahigh-energy protons can reconcile the results of the VERITAS and Fermi observations.