La Liga 'Clasicos' set for October and March
Champions Real will then host Barca, who finished second last season, on the weekend of March 2/3, the RFEF said.
The great rivals also meet over two legs next month in the Spanish Super Cup, the traditional season opener that pits the league champions (Real) against the King's Cup winners (Barca).
The first leg will be played at the Nou Camp on August 23, with the return at the Bernabeu on August 30, the RFEF said.
Real begin the defence of their La Liga title at home to Valencia, third last term, on the weekend of August 18/19, while Barca are at home to Real Sociedad.
"It's going to be a tough season, like the last one, and we will try to respond to expectations with the support of our fans," Real director Emilio Butragueno said during the draw.
Jose Mourinho's Real set a points record of 100 in winning the title for the first time in four years last season, when they ended Barca's three-year reign as champions.