The 31-year-old linked up with his national side on Monday for the World Cup qualifiers with Iceland, Romania and North Macedonia.
However, Germany confirmed on Wednesday (AEDT) that Kroos has returned to Madrid as a precautionary measure and will play no part in any of its games over the next eight days.
"Our medical department has examined and treated Toni intensively," said head coach Joachim Low, who will step down from his position at the end of the rescheduled Euro 2020 tournament.
"He would have liked to stay with us, and I am reluctant to be without him. But with a view to the Euros, we decided that the full recovery from this injury must be a priority."
Kroos earned his 100th cap for Germany in October's 3-3 draw with Switzerland and has featured 35 times in all competitions for Madrid this season.
He previously missed two games earlier this season with a gluteal injury, seeing him play no part in the league wins over Real Valladolid and Levante.
Germany are also without Niklas Sule and Robin Gosens for Thursday's clash with Iceland in Duisburg, the pair unavailable with thigh and muscular problems respectively.
The build-up to the match has been dominated by talk of who will succeed Low as the next Germany head coach, but Manuel Neuer insists it will be business as usual on the field.
"We had a short team meeting and are concentrating on our tasks," he said. "We have to be well prepared for the European Championship and will use every game to do that.
"We cannot make any more mistakes. We have a strong group, against some strong opponents, so every game is a final from the start.
"Of course now we want to crown this era with a success. The coach deserves that to end with a success after the successful years.
"He is is very motivated and ambitious. It's not that he thinks he's going to retire. He's enthusiastic. He wants to quit as national coach as successfully as possible."
Under-21s boss Stefan Kuntz is among the frontrunners to replace Low, who has been at the helm since 2006 and guided his country to World Cup success in 2014.
Ralf Rangnick and Hansi Flick, who manages Neuer at club level with Bayern, are also in the running, while Jurgen Klopp and Julian Nagelsmann have distanced themselves.
Asked about the candidates for one of the top jobs in football, Neuer said: "A national coach must have experience and must have done one or the other in German football.
"He should know the Bundesliga. It's not about what we think, but about the goals that we have in front of us."