The supporters were both involved in incidents at the same bar on Tuesday night, though they are believed to have been separate instances.
Though the fans have been hospitalized, neither injury is thought to be serious.
Chelsea is conducting an investigation into the incidents and collecting evidence alongside the British Consulate, which is also involved in the process, though responsibility lies with the local Turkish police.
There is a significant precedent to this situation with clashes between Leeds United and Galatasaray fans before a UEFA Cup match in 2000 resulting in the death of two fans of the now-Championship club.
Chelsea faces Galatasaray on Wednesday evening.
- Sports & Recreation