According to a spokesman, McAveety is leaving to pursue other opportunities in Europe.
He will be replaced by Brent Scrimshaw, general manager of Nike US East business, who worked under McAveety between 2001 and 2004 as EMEA brand initiative director. Scrimshaw will move from New York to take up the role at Nike's European headquarters near Amsterdam.
McAveety joined Nike in 1997 as advertising director for Asia Pacific and rose to vice-president EMEA marketing in 2001.
Adidas sold 3m replica shirts in the four months leading up to the start of the World Cup, outselling Nike's 2.4m - the first time the latter has lost out to Adidas in the run-up to the tournament.