The club announced that Kroos returned a positive test on Monday, having missed Sunday's win at Athletic Club after coming into direct contact with someone who contracted the virus.
"Real Madrid C. F. announces that our player, Toni Kroos, tested positive in the COVID-19 test he underwent today," read a club statement.
"Kroos has been in isolation since Friday May 14 after having come into direct contact with someone who tested positive for COVID-19."
Real Madrid are second in the standings, two points behind leaders Atletico Madrid, ahead of their decisive final game at home to seventh-placed Villarreal on Saturday.
Atleti travel to relegation-battling Real Valladolid at the same time, knowing a win would guarantee their first league crown since 2013-14.
Kroos has been a key member of Zinedine Zidane's Real squad this term, scoring three goals in 42 games in all competitions.