Several shots were fired at the front of the club's bus after Saturday's 5-1 win at Rizespor and the driver was subsequently rushed to hospital with facial injuries, though he appeared conscious in photos and videos posted online.
The club were quick to condemn the attack, while Super Lig officials also spoke out about the incident while confirming an investigation will be launched.
Ahead of an emergency meeting scheduled for Monday, a Fener statement on Sunday suggested exactly what measures should be taken.
"We believe that, as long as this attack is not solved in a way that satisfies Fenerbahce and public opinion, a suspension of the championship is inevitable," the Istanbul club posted.
"Blood ran and football was silenced. Finding and punishing the culprits is of vital importance for Fenerbahce."
The incident occurred as Fener's team bus drove through Trabzon and local club Trabzonspor also issued a statement on the attack.
"It is impossible to describe this," club official Yakup Aslan told Hurriyet.
"As a club, we are not going to let this incident slide. We will do whatever it takes to ensure that this person or people are caught and handed over."
