The short answer is "no." But a new study in PLOS One suggests that some monkey calls may be morphologically-complex. Here is the relevant passage:
Some calls were given to a broad, others to a narrow range of events. Crucially, “krak” calls were exclusively given after detecting a leopard, suggesting that it functioned as a leopard alarm call, whereas the “krak-oo” was given to almost any disturbance, suggesting it functioned as a general alert call. Similarly, “hok” calls were almost exclusively associated with the presence of a crowned eagle (either a real eagle attack or in response to another monkey's eagle alarm calls), while “hok-oo” calls were given to a range of disturbances within the canopy, including the presence of an eagle or a neighbouring group (whose presence could sometimes be inferred by the vocal behaviour of the females).
The authors take this as evidence that "oo" is a suffix of some sort that modifies the meaning of the preceding part of the call.
Maybe. Whether two words that contain similar sounds share a morpheme or not is an old problem in linguistics, and one that is actually hard to solve. I cut my teeth on such questions as whether the /t/ in swept is the same past-tense affix that we see in dropped. Notice that both words end in the sound "t" -- but, then, so does "hat," and probably nobody thinks the /t/ in "hat" is a suffix.
One crucial test the authors would need to do would be to show that this "oo" suffix can be used productively. If this was a study of humans, you might teach them a new word "dax," which refers to a chipmunk, and then see if "dax-oo" was interpreted as "warning, there's a chipmunk!"
All of which is not to say that this isn't an intriguing finding, but we're a ways from talking monkeys yet.