The short answer is no; there is no requirement that you be a U.S. citizen or resident to start a nonprofit corporation. In practice, it may be difficult to run a corporation from abroad; however, there is no legal requirement that the incorporators be citizens or maintain residency, and the process for incorporating for foreigners is the same as for U.S.-born citizens.
Still, you may want to consider if incorporating is even necessary or a good idea for your business. For example, if you plan to operate only on the Internet without a physical address in the U.S., then incorporating may not be required. Also, it is important to do a cost comparison analysis between incorporating in the U.S. and keeping operations in your home country. Often, transportation costs, state taxes, trade regulations, and the local capital required for conducting domestic operations in the U.S. outweigh the potential benefits.