how can I prevent sawdust from falling on my clean dishes?

I have old cupboards in my kitchen that look like they were hand built. The problem is that when I go to take out my bowls or other items to use to prepare a meal, there will be sawdust in them. I suspect that this may be from opening and closing the drawers at the top of the cupboards, but am not exactly sure. These cupboards are all wood. There is no laminate, or pressed wood or anything like that. I think they are perhaps maple but again am not sure.