The 29-year-old picked up the knock in the latter stages of the defeat at Aston Villa before the international break, and he did not feature for the Ivory Coast as a result.
He described the injury as "improving" but was late for an appearance at the Support for Africa charity, who are hosting a concert later this month where Drogba is possibly featuring as a guest singer.
"I'm not really fit," he said. "I was late because I had to stay to have some treatment and we had a meeting."
The concert on September 23 at the Royal Albert Hall - which is titled Football Reaching Out For Africa - is on the same day as Chelsea's clash against Manchester United and Drobga wants to travel straight there to make his appearance if he is playing.
Drogba talked about the injury, revealing that he had been troubled by it since the start of the campaign but it flared up at Villa Park.