Geopolymer concrete possesses superior fire resistance compared to ordinary Portland cement (OPC)-based concrete; however, there are concerns regarding its vulnerability when exposed to real fire events. In the present study, the fire resistance of fly-ash-based geopolymer concrete was evaluated relative to that of OPC-based concrete. Concrete specimens of standard strength grades of 20, 40, and 60 MPa were exposed to fire at 500 and 1200 °C for 2 h to simulate real fire events. Visual observation was performed, mass loss and residual compressive strength were measured, and scanning electron microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR) analyses were conducted. OPC-based concrete suffered major cracks accompanied with spalling for the high-strength specimen, while geopolymer concrete experienced minor cracks with no spalling. Mass losses of the geopolymer concrete—of 1.69% and 4%, after the exposure to fire at 500 and 1200 °C, respectively—were lower than those of the OPC-based concrete. More than 50% of the residual compressive strength for low- and medium-strength geopolymer concrete, after the exposure to fire at 1200 °C, was maintained. After the exposure to fire at 500 °C, the residual compressive strength of the geopolymer concrete increased from 13 to 45%, while the OPC-based concrete was not able to sustain its compressive strength. SEM images showed that the matrix of the geopolymer concrete, after the exposure to fire, was denser than that of the OPC-based concrete, while the FTIR spectra of the geopolymer concrete showed a minor shift in wavelength. Hence, our findings indicate that fly-ash-based geopolymer concrete has an excellent fire resistance as compared to OPC-based concrete.