The Ukrainian club attributed the shocking incidents to "shelling", with the eastern city currently serving as a battleground between national forces and pro-Russia separatists.
No one was hurt in the two explosions, but Shakhtar revealed on their official website the extent of the damage.
A club statement read: "On 23 August, at 6:00, two powerful explosions occurred at Donbass Arena. As a result of shelling, there are numerous damages of the northwestern facade of the stadium, communications, equipment and detached building of the energy centre, which is located in the northern part of the Donbass Arena park."
As yet there is no indication that the stadium, which hosted games during Euro 2012, was deliberately targeted.
Shakhtar are due to compete in the group stages of the Champions League - with their home matches to take place in Lviv in the west of the country.
Donetsk is one of the key battlegrounds in the military confrontation which has erupted in eastern Ukraine.
- Sports & Recreation