Murdoch was praising Republican presidential candidate Ben Carson and his wife on Twitter on Wednesday evening when he wrote:
"Ben and Candy Carson terrific. What about a real black President who can properly address the racial divide?"
Later, Murdoch recommended a New York magazine article asking whether Obama has done enough for the African-American community.
Murdoch is the founder of Fox News Channel, and News Corp's publications include The New York Post and The Wall Street Journal.
Murdoch, 84, has praised Carson on Twitter before, calling him "irreproachable on background, achievements, character, vision".