Quick Answer: No, you shouldn't microwave wood. At least, there's no way to go about doing it with absolute safety, as you're about to learn.
But let's find out a little more about wood first...
Related Article: Can You Microwave Styrofoam? (Here's What You Need to Know)
Different Types of Wood Containers and Utensils
How Do You Know If Wood Is Microwave Safe or Not?
Labels on WOod to Be Aware Of
Any item that can be microwaved might have a "microwave safe" label on the bottom. Look on the packaging it comes in as well.
There could also be a label that shows that the item is not intended for microwave use. Either one of these labels is highly valuable and will tell you right away whether you can microwave a product or not.