The Ukrainian club confirmed that the north-western side of the stadium was hit by "two powerful explosions" that occurred on Saturday morning.
"On August 23, at 06.00 [08.00BST], two powerful explosions occurred at Donbass Arena," said a statement on the club's official website.
"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.
"There are no casualties among the stadium staff."
The news comes one month after six Shakhtar players – Fred, Ismaily, Douglas Costa, Alex Teixeira, Dentinho and Facundo Ferreyra – refused to return to Ukraine because of the unstable political situation in the country.
The reigning Ukrainian Premier League champions recently revealed that they will not be able to host games at the Donbass Arena because of violent clashes and will instead play their home matches in Lviv for the upcoming season.