Fenerbahce will play on Thursday after almost a two-week absence following the gun attack on their team bus, which led to the suspension of Turkey's SuperLig.
The club, who have agreed to face Mersin in the cup after receiving security assurances from the government, had initially stated they would not play until the crime was solved.
Turkish football chiefs claimed the 4 April attack was "terrorist" related.
The SuperLig resumes on Friday.
Fenerbahce will play its next league match on Monday against Bursaspor.