Dear Nina,

What you have here is a Japanse Inro. https://en.wikipedia.org/wiki/Inro
Yours is made of wood and lacquer and and has I think an Ivory ( or a nut ) Ojime ( cord fastener ). The netsuke ( the ens knod ) is made of boxwood most likely.
This Inro was used as a medicine container.
Your inro is really nicely painted and looks in great condition. It is made in Meiji period and I believe around 1900. Some things from Japan are still highly collectable and the Inro is one of them. I believ if your Inro came to auction I expect it to make a price around the estimate.