More than 10 billion messages a day pass through Facebook's messaging products

"Q - On the other hand, WhatsApp is huge — huger than Facebook’s Messenger. And you bought that because you think it will move the needle someday. So, tell me about that acquisition, but also tell me: Why couldn’t Facebook invent that? Do you worry that Facebook didn’t invent that?
A - Well, so there are a bunch of things here. One thing is that Facebook Messenger is actually a really successful thing. More than 10 billion messages a day that flow through Facebook’s messaging products. But I think we basically saw that the messaging space is bigger than we’d initially realized, and that the use cases that WhatsApp and Messenger have are more different than we had thought originally. Messenger is more about chatting with friends and WhatsApp is like an SMS replacement. Those things sound similar, but when you go into the nuances of how people use it, they are both very big in different markets."
Source:  Interview with Mark Zuckerberg in the New York Times, 16th April 2014
Update - 200m active monthly users on Facebook Messenger