The Germany international had to be substituted in first-half stoppage time in Seville, Luka Modric coming on to replace his fellow midfielder.
Following tests on Monday, Madrid announced Kroos has an issue in the gluteal region, though did not reveal how long the 30-year-old will be sidelined.
“Following tests carried out today on our player, Toni Kroos, by the Real Madrid medical services, he has been diagnosed with a muscular injury to the left gluteus medius," a statement from the club read.
"His recovery will continue to be assessed."
Zinedine Zidane's squad are next in action on Wednesday, hosting Real Valladolid, while the reigning champions travel to Levante at the weekend.
Kroos could also be a doubt for a trio of upcoming international fixtures. Germany play Turkey in a friendly on October 7, followed by Nations League games against Ukraine and Switzerland during the break.