This story has stayed with me for a long time.
Published in a 1970s (possibly '60s) issue of F&SF.
Post-apocalypse setting -- no devastation described, but people live in low-tech hunter-gatherer tribes. Protagonist is a hunter. In a time of need, when no other game can be found, he does what his father did before him: secretly goes to an old high-tech facility, holding pre-disaster humans frozen in individual cases (probably some kind of cryo-preservation, although our hero obviously doesn't know this). He breaks open a capsule, butchers the person inside until the meat is no longer recognizable as human, and brings it back to the tribe.
The story ends when he unpacks his leather bag of meat and a human hand tumbles out.
