We investigate the detectability of a proposed population of gamma-ray bursts (GRBs) from the collapse of Population III (Pop III) stars. The James Webb Space Telescope (JWST) and Space Infrared Telescope for Cosmology and Astrophysics (SPICA) will be able to observe the late time infrared afterglows. We have developed a new method to calculate their detectability, which takes into account the fundamental initial mass function and formation rates of Pop III stars, from which we find the temporal variability of the afterglows and ultimately the length of time JWST and SPICA can detect them. In the range of plausible Pop III GRB parameters, the afterglows are always detectable by these instruments during the isotropic emission, for a minimum of 55 days and a maximum of 3.7 yr. The average number of detectable afterglows will be 2.96× 10-5 per SPICA field of view (FOV) and 2.78× 10-6 per JWST FOV. These are lower limits, using a pessimistic estimate of Pop III star formation. An optimal observing strategy with SPICA could identify a candidate orphan afterglow in ∼1.3 yr, with a 90% probability of confirmation with further detailed observations. A beamed GRB will align with the FOV of the planned GRB detector Energetic X-ray Imaging Survey Telescope once every 9 yr. Pop III GRBs will be more easily detected by their isotropic emissions (i.e., orphan afterglows) rather than by their prompt emissions. © 2013. The American Astronomical Society. All rights reserved..