We spoke with international tax reporting specialist Ms. McCormick (#1000349089) about your question. We are assuming that you are considered a non-resident alien for tax purposes.
That said, there are two broad questions that must be addressed: 1) Is the fellowship taxable? 2) Do you need to submit a U.S. tax return?
As to the first, IRS Publication 970, Tax Benefits for Education states on page 5 that a fellowship is tax free if it doesn't exceed your qualified education expenses, doesn't go toward anything other than qualified education expenses (such as room and board, which portion is taxable), and doesn't require that you provide teaching or other services as a condition for receiving the fellowship.
If you aren't sure of your tax status, or whether or not you need to file a return at all, refer to Publication 519, U.S. Tax Guide for Aliens. If you do need to file, the form you would use is 1040-NR.
Ms. McCormick did explain that they have a questionnaire they generally run through with a caller on these matters, and since we didn't know the answers to many of those questions, we suggest you call the IRS directly yourself for better guidance; the number is (267) 941-1000. Select your language preference, then press 4 at the second prompt, and then 4 again at the third prompt.