FIG. 1 is a perspective view of a protective sleeve device for vials showing my new design;

FIG. 2 is a front view thereof;

FIG. 3 is a back view thereof;

FIG. 4 is a side view thereof;

FIG. 5 is an opposite side view thereof;

FIG. 6 is a top view thereof; and,

FIG. 7 is a bottom view thereof.

The broken lines in FIGS. 1. 2, 4, 5 and 7 are included for the purpose of illustrating portions of the protective sleeve device for vials that form no part of the claimed design.