Am I eligible for a fellowship doing interdisciplinary work? I'm pondering a Masters (thesis) in Computer Engineering after I graduate undergrad. I also have a subject matter I want to research that will probably require a fellowship in order to conduct my Masters.

I want to explore a section of Computer Engineering that I can apply to Sociological and Ethnic studies ( the particulars of what that is isn't important here ). I have a sociological research institute  in mind that is perfect to help my research into what I want to do for my Masters. I want a fellowship in this institute because its the preeminent leader in its field and it intersects perfectly with what my research would be about. 

The thing is, I don't know if they would even take me in the first place. Yes, I have a degree in Sociology but my Masters work is in engineering. Would it be in the norm for a research institute ( especially one in the Social Sciences ) to offer a fellowship to someone who isn't in their field? I'm going to be a Engineering Master's student who wants to conduct research in a Social Science field.
You sound like a perfect candidate, given your major and your further plans. Many social scientists like to understand problems more than fight about academic boundaries--at least if they are at an institute that describes itself as concerning the "Social Sciences" rather than a particular discipline. 

Do look carefully at the guidelines to see if they specify which programs they will support. If they are vague, you may want to ask the program officer for the fellowship about whether it is designed to fund such cross-disciplinary study, and/or if there are "computational social science", etc. programs to apply to that would be purely in scope. (You can look at lists of past awards to see the variation so far.)

If you have a strong start in computer engineering and you can convincingly convey your dedication to use it for the social science purpose you mention, as well as show that the degree program will let you, then you could be a strong candidate. (Unless the fellowship is specifically toward master's degrees, you may face tough competition from doctoral students, though not because you are on the wrong track.) Good luck!