The Dow Jones website AllThingsD, citing a source familiar with the matter, reported that Rich Williamson was fired last week in an extension of a shakeup at the California tech giant begun a month ago.
Apple did not respond to an AFP request for comment.
The news comes a month after Apple announced the departure of its head of the mobile software unit, Scott Forstall, as well as retail chief John Browett.
Apple last month said it was promoting other executives including Jon Ive, Bob Mansfield, Eddy Cue and Craig Federighi to better integrate hardware, software and services.
Apple has in recent months launched the iPhone 5, the mobile operating system iOS 6, iPad mini, and new versions of the iPad, iMac, MacBook Pro, iPod touch and iPod nano.
Apple was forced to make a highly embarrassing apology in September for its glitch-ridden maps application in the new operating system used by the iPhone 5 and urged customers to use rival programs while improvements are made.
Apple developed its own mapping program included in its new mobile iOS 6 operating system, and in doing so booted off Google Maps, which had been the default program for Apple devices.
But the new Apple program immediately drew scorn for omitting key landmarks and cities, failing to identify correct locations and distorting views from its images.