The team, which won the recent Champions League final against crosstown rivals Atlético Madrid, were handed the penalty because of fan behaviour during their 1-0 win over Bayern Munich on April 23th.
"Following the charge of racist behaviour by Real Madrid supporters during the match (Article 14 of the UEFA Disciplinary Regulations), the Control and Disciplinary Body has ordered the partial closure of the Santiago Bernabeu for one match," world football's governing body UEFA said in a statement.
"More specifically, sectors 120 and 122 of the stadium will be closed for the club's next UEFA competition home game.
"Real Madrid are obliged to display a banner with the wording 'No to Racism' in those sectors."
The Liga side are currently being investigated by UEFA after incidents in the final against Atletico, with more penalties possible.
The partial closure of the Santiago Bernabéu stadium is the latest racism scandal to hit Spanish sport.
Jewish associations in Spain's Catalonia region recently filed an official complaint after nearly 18,000 anti-Semitic messages were posted on Facebook and Twitter in response to Israeli basketball team Maccabi Tel Aviv's victory over Real Madrid.
In another footballing incident, International outrage erupted after a banana landed on the pitch near 30-year-old Brazilian FC Barcelona player Dani Alves during a league clash at Vilarreal's home ground of El Madrigal on April 27th.
Brazilian star Alves won praise for nonchalantly picking up the banana and taking a bite before setting up a goal to help Barcelona come from behind to seal a 3-2 victory.
A week later, Pape Diop, a 28-year-old Senegalese player for Liga side Levante, reacted by dancing when he was targeted by monkey chants during his side's 2-0 victory over Atletico Madrid.