The bus driver was taken to hospital with facial injuries after shots were fired at the front of the vehicle in Trabzon as the team made their way home from a victory at Rizespor in the Super Lig.
Trabzon governor Abdil Celil Oz confirmed the two people were apprehended in the Surmene region of the city.
Following the incident, Fenerbahce called for the top flight to be suspended - a plea answered by the Turkish Football Federation (TFF).
TFF officials confirmed on Monday that the league will be halted for a week with scheduled cup quarter-finals also postponed.
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