Sorry, but it is definitely not from a (pocket-size) sundial... because sundial numerals/numbers are not evenly spaced around the dial, nor do sundial numerals/numbers form a complete circle around the dial. See the sundial photo below.
Similar discs with numbers have turned up in this forum and been identified as a Post Office box's combination-lock dial. But your mystery-object, having Roman Numerals (rather than numbers) arranged in complete circle, would seem to be timepiece related... perhaps from an early wristwatch, or a ladies' pendant (necklace) clock.