Kroos will miss Real Madrid's trip to Real Betis in La Liga this weekend, but the Spanish and European champions have not placed a timescale on the German international's recovery.
The 28-year-old is reported to have picked up the problem in the first half of Wednesday's 3-1 win over Paris Saint-Germain in the Champions League, but still went on to play the full 90 minutes of the last-16 first leg.
"Following tests carried out on Toni Kroos by the Sanitas Real Madrid Medical Services, he has been diagnosed with a sprained to the exterior lateral ligament in the left knee," read a statement on Real Madrid's official website. "His recovery will continue to be assessed."
Kroos has scored four times and provided seven assists in 29 appearances for Madrid this season.