The French manufacturer said he would remain available to the company for a smooth transfer of power.
He has been CEO of Areva since June 2011.
In a statement, Oursel said, "I must now fight a personal battle against the illness, but all of my thoughts remain with the teams at Areva."
He became President and CEO of Areva Nuclear Power in 2007 before moving up to chief operating officer in January 2011.
Areva is due to release its quarterly figures this week.