His departure is the latest in a series of senior personnel changes at the newspaper publisher since Rebekah Brooks became chief executive in June.
Brooks, who was editor of The Sun before her promotion, now reports directly to Rupert Murdoch and oversees all NI's senior marketers.
Schwartz headed marketing across all the company's newspapers, including The Sun, The Times and the News of the World, before his exit.
It is not known if he has a job to go to. An NI spokeswoman said he would not be replaced for the foreseeable future.
Schwartz's departure means recent recruit Alex Lewis, who joins later this month as marketing director for The Times and The Sunday Times, and Kathy McAllister, interim marketing director for The Sun and News of the World, will be NI's most senior marketers, reporting directly to Brooks.
In March, Katie Vanneck was appointed to the new role of managing director of customer direct, where her remit is to drive take-up of NI products such as The Sun Bingo and The Times Culture+.
Earlier this month, three senior marketers were promoted and now report directly to Vanneck. Rob Painter was given the role of NI portfolio, strategy and planning director. His previous post of insight director has been filled by Mark Goodison. Martin Pierson was appointed creative director within media.
In another change of personnel, Mike Anderson, an NI executive and former managing director of The Sun and News of the World, left this month to start a consultancy. He will continue to advise The Sun on commercial matters.
Following Brooks promotion, The Sun's deputy editor, Dominic Mohan, was appointed editor, and associate editors Simon Cosyns and Geoff Webster were promoted to share Mohan's previous role.
NI owner Rupert Murdoch has announced plans to move toward a paid-content model across all the company's titles. Last month, it was announced that NI's free title, thelondonpaper, would close.
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