I don't believe the NFL has an official roster minimum, and the
NFL Rules Digest offers the following related information:
On defense, I suppose this means one could theoretically deploy zero players onto the field. Presumably one would need at least two players on the roster to compete on offense (and at least one on most special teams plays), however, as NFL rules mandate that a play must start with a snap, a free kick such as during kickoffs and safety punts, or the infamous "fair catch free kick" rule which is rarely if ever invoked.