Stuck gear hub on the way into a gear on an internal geared hub
Internal gear hubs are full of sproingy bits. This is what a Shimano gear hub looks like inside:



If that doesn't dissuade you, then you should know that Shimano doesn't generally sell replacement parts**. About the only thing that Shimano lets you do is change the oil and the bearings. If the hub is still under warranty, then Shimano will replace it in its entirety rather than trying to fix it. If it's broke out of warranty, then Shimano says: "Sorry, you should have bought a Rohloff."

** Your mileage may vary. As krzski notes, some Shimano dealers in some countries may have spare parts. 

Rohloff does have replacement parts but Rohloffs rarely break. Here's one person's take-apart of a Rohloff hub:



The three-speed Sturmey Archer internal gear hubs are a bit less complex, but still I wouldn't take one apart for the lulz.



But before you give up hope, take your bike to a bike shop. It may be as simple a matter that your indicator spindle or shifter cable needs adjusting. Sheldon Brown has very good instructions on how to adjust this (e.g., for Shimano Nexus) but we'd need to know which unit you had for us to give you details here. 

Update: You've clarified you have a Microshift shifter, which is commonly used on Shimano IGHs. Follow Sheldon's instructions on adjustment first before attempting repair. Another valid option is to pretend that your bike just doesn't have those gears and to live with it.