Germany Women captain and Lyon midfielder Dzsenifer Marozsan has a pulmonary embolism, which occurs when a blood vessel in the lungs is blocked.
The 26-year-old said in a statement on Facebook that she would be out of training "for a few weeks".
Germany travel to group leaders Iceland in their crucial, penultimate Women's World Cup qualifier on 1 September.
The two-time World Cup winners are one point behind Iceland, with one automatic qualification spot available.
"The most important thing now is that she will be completely healthy again," Germany coach Horst Hrubesch told the national team's website.
"She has our full support and should take all the time she needs."
Marozsan said she has been "receiving very good medical care here in Lyon", adding: "The people who know me know that I am a fighter and will come back even stronger."
Lyon will meet Manchester City in Miami on Thursday, 26 July in the new Women's International Champions Cup pre-season event, in a repeat of last season's Women's Champions League semi-final.