Fenerbahce were travelling back from Saturday's 5-1 win at Rizespor when several shots were aimed at the front of the bus.
The driver was taken to hospital with facial injuries, although photos and videos posted online appeared to show he was conscious.
Fenerbahce's players were said to be unhurt in the incident, but the club condemned the attack and called for the league to be suspended.
Super Lig officials confirmed that an investigation would be launched and the Turkish Football Federation has now stated that the league will be halted for a week, while scheduled cup quarter-finals have also been postponed.
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