Minimum order quantities (MOQs) for custom packaging vary based on the exact supplier and manufacturing process you choose, but these are the ballpark numbers.
MOQs are usually based on the tooling costs and setup costs a factory needs to produce your custom packaging. For example, flexo-printed die cut corrugated boxes have a minimum quantity of 1,000 units because it costs roughly as much in setup costs to make 1,000 units as it does to make any fewer. If you are producing overseas, a similar notion applies to freight shipping, meaning sometimes the costs of shipping from Asia make it just expensive to order small quantities as larger quantities.
You will find the lowest MOQs on products that can be digitally printed, because these do not require tooling.