The present work aims to explore the impact of solar gamma-ray flares (GRFs), detected by the Fermi-Large Area Telescope (LAT), and their associated X-ray flares (XRFs) on the Earth’s lower ionosphere. The data of ionospheric parameter fmin were collected from the Yamagawa mid-latitude ionosonde station in Japan. Because most of the GRFs used in this study are associated with soft X-ray (SXR) emissions, detected by the Geostationary Operational Environmental Satellite (GOES), we classified them into three types: simultaneous (S), delayed (D) and not associated (N), reflecting the phase occurrence of the solar flares. Generally, the ionospheric D layer responds strongly to XRFs more than GRFs. The temporal profiles of the ionospheric parameter fmin show distinct behaviors as a response to the various GRF types. In the case of the S-type, a single strong peak, with an average value of 5.2 MHz, emanates in the fmin profile within an average interval of time of less than half an hour. In the case of the D-type, two successive peaks appear in the fmin profile, with an average value of 6.0 MHz for the second peak through a time interval of one hour after the onset of gamma-ray (GR) emissions. The response of the fmin parameter to the N-type flares appears as a single peak with an average value of 4.8 MHz within about an hour. We notice that the difference between the fmin peak values and the corresponding reference ones (dfmin) is more convenient and representative than the fmin values, where the median GR flux of the S-, D- and N-types tends to increase as the average dfmin increases.