The binding of the TRIM5α restriction factor to the HIV capsid is mediated by the C-terminal SPRY domain of TRIM5α. Atomic-level details of this host-pathogen interaction, which involves mobile variable loops of the SPRY domain, remain unclear. Some of the key determinants of restriction are encompassed by the long and disordered v1 loop of the SPRY domain. We applied molecular modeling to elucidate the conformational repertoire of the v1 loop and its role in the interaction with the capsid. All-atom replica exchange molecular dynamics revealed multiple transient, interconverting states of the v1 loop consistent with the intrinsic disorder observed experimentally. The docking of the SPRY conformations representing 10 most populated states onto the high-resolution model of the assembled HIV-1 capsid revealed that a subset of v1 conformations produced plausible binding poses, in which the SPRY domain binds close to the pseudo-2-fold symmetry axis and the v1 loop spans the interhexamer gap. Such binding mode is well supported by the NMR binding data and known escape mutants. We speculate that the binding mode that involves interaction of the capsid with a subset of preexisting SPRY conformations arising from the intrinsic disorder of the v1 loop may explain the remarkable ability of TRIM5α to resist viral evasion by mutagenesis and to restrict divergent retroviruses.