The company does not immediately plan to fill Cox's role, Zuckerberg said, adding that Cathcart, Simo and the heads of Instagram and Messenger will now report directly to him.
Cox joined 13 years ago and helped create Facebook's News Feed feature.
"This will be a big project and we will need leaders who are excited to see the new direction through", Cox said in a Facebook post. Chief Product Officer Chris Cox and Chris Daniels, who heads messaging app WhatsApp, are departing.
The move comes with Facebook struggling to cope with investigations and complaints over data protection and privacy, and after Zuckerberg's announcement last week of a new focus for the platform.More news: Flu season is not over yet
The move will more tightly integrate the three apps - a move that critics say could have potential antitrust implications and which reportedly has sparked disagreement among some of Facebook's senior employees.
Zuckerberg phrased that more delicately, noting that "We both realized we had too much important work to do to improve our products for society". The longtime Facebook executive Will Cathcart will head up WhatsApp.
Cox and Daniels are among a string of executives who've left Facebook since 2017.
"At this point, we have made real progress on many issues and we have a clear plan for our apps, centered around making private messaging, stories and groups the foundation of the experience, including enabling encryption and interoperability across our services", Zuckerberg continued.More news: Is Lori Loughlin's Daughter Olivia Jade Getting Expelled For Bribery Case?
While Zuckerberg also said that Cox had spoken before about his desire to leave the company, that his departure is tied directly to Facebook's so-called privacy pivot, is significant.
Cox's departure removes a layer of management, bringing Zuckerberg closer to a family of apps that he wants to make compatible.
Originally published March 14, 1:19 p.m. Update, 1:48 p.m.: Includes more background and Zuckerberg's post to employees; 1:55 p.m.: Adds background about other executive departures; 2:15 p.m.: Includes post from Chris Cox.More news: Released Testimony Shows Obama DOJ Told FBI Not to Charge Clinton