McKinney, formerly head of news and current affairs at Scottish TV, joined the charity in January as head of media, his first PR role (PRWeek, 14 January).
Oxfam deputy head of media Sam Barratt has been promoted as McKinney's replacement. He said McKinney had left for 'personal reasons'.
McKinney, who began his career as a researcher for Gordon Brown in the 1980s, could not be reached for comment.
In another move, Oxfam head of advocacy Phil Bloomer has been promoted to the post of campaigns and policy director. He replaces Justin Forsyth, who left in December to work as a special adviser to the Prime Minister on international development .
Acting campaigns and policy director Becky Buell will return to her post as programme policy director.
Barratt will lead a 14-strong department, reporting to Bloomer.
He will focus on stepping up Oxfam's international media coverage, raising the profile of its shops and appeals, and increasing celebrity support.
Current campaigns include Make Poverty History, Make Trade Fair and Control Arms, as well as emergency response for regions affected by the Asian tsunami and unrest in Darfur.
Barratt is a former account manager at Midnight Communications.