The driver was hit in the face and taken to hospital, the club`s vice president Mahmut Uslu said.
Mr Uslu, who was on the bus at the time, accused the attackers of trying to "crash the bus and kill the players".
Fenerbahce midfielder Mehmet Topal told reporters: "We cheated death. God protect us. I hope our driver will be all right. Words fail me. It`s unbelievable."
The vehicle was hit as it drove to the airport following the team`s 5-1 away win at the Black Sea side Caykur Rizespor in Turkey’s Super Lig.
There was no mention of any injuries to anyone else but the driver.
Several pictures of the bus were posted on the club`s website, revealing a shattered side window and damage to the front windscreen.
The pictures also showed blood on the driver`s seat and the steering wheel.
The bus was going over a viaduct on its way from the city of Rize to the airport in Trabzon to return to Istanbul.
Trabzon governor Abdil Celil Oz confirmed the gun attack on the bus and said the driver`s life was not in danger.
"At first we thought stones had been thrown at the bus but forensic investigators at the scene have concluded it was an armed attack," he said.
The governor said he had received a phone call from President Recep Tayyip Erdogan, a supporter of the Istanbul club, asking him about the investigation.
The Turkish Football Federation released a statement condemning the attack.
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