It looks like an Indo-Persian slow-match box. Slow matches were used to ignite the powder in the pan of a matchlock, which in turn caused the gun to fire. A spare length of slow-match was carried coiled in the box; powder and ball were often carried in wooden containers called cartridges which were hung from belts worn over the the shoulder. As the matchlock musket remained popular in India (as well as Japan and China) longer than it did in Europe, most of the slow-match boxes encountered tend to come from the sub-continent hence the Indo-Persian attribution.

That said, without actually examining the item, this is nothing more than a semi-educated guess.