Shakhtar is demanding 50 million euros in damages for lost transfer fees.
The club filed an appeal with the court.
The chief executive of Shakhtar said that they had to do this because of the ruling of the world governing body.
We will continue to lose money from deals we expected to close.
Given the situation Ukrainian clubs are facing with the war, there has been little respect shown to these clubs by the world governing body.
The perilous state that Ukrainian football clubs have been facing since the beginning of the war has not been looked at by the Federation of International Football Associations.
Shakhtar lost money on four players who left the club after their contracts were not renewed.
"FC Shakhtar has lost a chance to transfer four foreign players for the total amount of about 50m, because of the decision of Fifa."
The four foreign players withdrew from the negotiations.
The players' agents advised them to leave the club in order to get more lucrative deals with new employers.
Foreign players and coaches can suspend their contracts with Ukrainian clubs if they don't reach an agreement with their club by 30 June.
Shakhtar had 14 foreign players in their squad and wanted to sell some of them in order to raise money.
Their revenue streams have been decimated by the Russian invasion and they had hoped to get some money back to cover their losses.
Buying clubs and agents waited to avoid paying transfer fees due to the fact that they had just over a week to conclude any deals with players.
In a letter to the CAS, Shakhtar said that the permanent transfers of Solomon and Lemos Martins were put on hold because of the ruling.
He accused agents of exploiting the war in Ukraine for their own benefit by stealing players and asking for fees to be paid directly to them rather than the club.
We will have no choice but to seek compensation from the competent courts if there is no response from Fifa.
There needs to be more meaningful support for Ukrainian clubs.
On April 27th, the top league in Ukraine was terminated due to the war.
The Fifa has been contacted by the British Broadcasting Corporation.