The browser component of the Android tablet is a built in software package. It cannot be easily removed, disabled, or otherwise hidden. However, there are other applications that you can download from the Play market that allow you to mask what applications your child can interact with. These applications, when downloaded, will allow your child only to have access to the parts of the tablet YOU say they can, and nothing else.
- Kids Place - Parental Control
- App Lock
While the three above are just the top three in the market that do what you want, there are plenty of others to choose from as well.
When sharing a tablet, phone, or smart device, it is wise to setup an environment that is safe for the other person while still keeping control. These applications allow you to specificy what you want shared, allowed, and available on the tablet, without affecting the operation of the machine. So, they should work for you quite well.