The sports newspaper report that Ekici picked up an injury during the Europa League qualifier against Differdange 03 and that his recovery will take another fortnight.
The Turkish international midfielder was statistically the Süper Lig player of the season according to Whoscored with a 7.71 rating.
The Turkish international midfielder hit the ground running in his first season playing in the Süper Lig racking up nine goals and making a name for himself as being a bit of a set piece expert.
Trabzonspor had a disastrous start to the seasons after getting knocked out in the Europa League qualification round against Macedonian side Rabotnicki.
The Black Sea Storm will face Bursaspor in their opening game of the season at the Avni Aker stadium.
Trabzonspor are currently managed by Shota Arveladze who replaced Ersun Yanal as head coach last month.