The 33 year-old striker was on holiday in France when he was found to have the virus, and it means he must isolate before heading back to Spain.
Benzema played for France in the Euro 2020 finals after being called up to Didier Deschamps' squad for the first time since 2015.
He scored four goals in four games, hitting doubles against Portugal and Switzerland, but could not help France advance any further than the second round, with the Swiss ousting Les Bleus in a penalty shoot-out after a 3-3 draw.
According to reports in Spain, Benzema is undergoing his quarantine period in Lyon.
A short statement from his club read: "Real Madrid CF confirm that our player Karim Benzema has tested positive for COVID-19."
Benzema has been Madrid's leading scorer in each LaLiga season since Cristiano Ronaldo left for Juventus in 2018, scoring 21 goals in 2018-19 and 2019-20 before improving to 23 goals last term, adding nine assists.
Madrid, who appointed Carlo Ancelotti to succeed Zinedine Zidane in June, begin their LaLiga campaign on August 14 with a match against Deportivo Alaves.
Looking to dethrone reigning champions Atletico Madrid in 2021-22, Ancelotti's team will step up pre-season efforts with a friendly against Scottish champions Rangers in Glasgow on Sunday.