No, but it's probably a good idea.
She is an American citizen with, presumably valid, American passport therefore she can travel on that passport. However, entering Mexico with an American passport generally limits stay to 180 days.
Traveling with the Mexican passport alone will require a US visa.
I recommend traveling with the US passport, but carrying the Mexican passport (or other document such as birth certificate) so that on returning back to Mexico you can show she is also a Mexican citizen and thus not subject to the stay limit for non-citizens.
