The Court of Arbitration for Sport has dismissed the Turkish club's appeal against a two-year competition ban which had been imposed by UEFA.
The CAS ruling removes Fenerbahce - beaten 5-0 on aggregate by Arsenal in this season's Champions League qualifying round - from the group stage of the Europa League.
UEFA expelled Fenerbahce in June after judging that club officials helped fix matches to win the 2011 Turkish league title. UEFA rules bar clubs which are implicated in fixing matches played since April 2007.
UEFA agreed to let Fenerbahce play Champions League matches pending the CAS verdict.