We calculate the solar-modulated energy spectra of cosmic-ray antiprotons ( p 's) from two candidate primary sources, i.e., evaporating primordial black holes and the annihilation of neutralino dark matter, as well as for the secondary p 's produced by cosmic-ray interactions with interstellar gas. A large enhancement toward the solar minimum phase emerges in the low-energy flux of p 's from the primary sources, whereas the flux of the secondary p 's, falling steeply below 2 GeV, does not significantly vary. This enables us to conduct a very sensitive search for primary p components by precisely measuring the p spectrum, especially at low energies, throughout the forthcoming solar minimum phase.