JSON.NET is licensed under the MIT License which allows you to use it any type of application without any restriction. By the way I am quoting you the following from the home site which I would recommend you doing if you use it in a commercial application (don't feel obligated of course):
Json.NET is a free open source project that has been developed over
hundreds of hours of my own time. If you are using Json.NET
commercially and you find Json.NET useful I'd appreciate donations to
help support future development. -JamesNK