Midfielder Kroos missed Sunday's 1-0 win over Athletic Club due to health and safety protocols having come into direct contact with a confirmed coronavirus case.
The Germany international had remained away from the club since Friday, when Madrid issued a statement revealing he had returned negative test results at that stage.
However, he will now miss the final game of the season for Los Blancos, who remain in the running to retain their league title in Spain.
"Real Madrid announces that our player, Toni Kroos, tested positive in the COVID-19 test he underwent today," a statement from the club read on Monday.
"Kroos has been in isolation since Friday, May 14 after having come into direct contact with someone who tested positive for COVID-19."
Madrid's triumph at the weekend leaves them still two points behind leaders Atletico Madrid going into the closing weekend of the campaign.
It had appeared Zinedine Zidane's side were going to take over at the summit, only for their city rivals to stage a comeback at home against Osasuna. Luis Suarez scored a late winner at the Wanda Metropolitano to grab a 2-1 triumph that keeps them in pole position.
Madrid host Europa League finalists Villarreal on Sunday, while Diego Simeone's Atleti travel to relegation-threatened Real Valladolid.
Kroos' health will also be of great interest to Germany coach Joachim Low, too, considering the delayed Euro 2020 tournament begins next month.
The former Bayern Munich player missed the World Cup qualifiers in March due to injury, meaning his most recent international appearance came in the 6-0 Nations League loss to Spain in November 2020.