The European champions said that the Croatian had a “partial tear of the adductor muscle tendon in his right leg”.
The 23-year-old limped off in tears to be replaced by Toni Kroos in just the 25th minute.
Spanish media reported on Thursday that Kovacic would be out of action for between one and two months.
His injury is just the latest problem for Real coach Zinedine Zidane ahead of Sunday’s La Liga clash at Real Sociedad.
Zidane is already without the suspended Cristiano Ronaldo and Marcelo for the match, as Real look to bounce back after drawing two of the first three games of their La Liga title defence.
French striker Karim Benzema is also out injured, while in-form youngster Marco Asensio missed the APOEL victory after reportedly suffering an infected pimple while shaving his legs, that Zidane said means “he cannot lift his sock”.
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