The news marks the third time in as many months that Shakhtar's home stadium has been hit by explosions as part of the continued unrest in Ukraine.
A ceasefire between the Ukrainian government and pro-Russian separatists had been enforced in Donetsk, which is currently under rebel control.
But that agreement now appears to have been broken, with the shelling causing significant damage to the western side of the arena.
A statement on Shakhtar's official website read: "Donbass Arena was seriously damaged in the course of the ongoing, continuous shelling of Donetsk.
"The western part of the stadium, facing Chelyuskintsiv Street, took the brunt of the attack. As a result, metal structures of the building were deformed and destroyed, window panes broken, communications damaged.
"The fact that the attack at the Donbass Arena, as, indeed, at the entire city, was made during the so-called truce, gives the incident a particularly cynical colouring.
"In connection with the incident, as well as the fact that the tension in the region does not ease off, being increasingly built up daily instead, FC Shakhtar voices the strong protest to all parties to the conflict. Destroying cities and towns and killing civilians is a terrible crime, for which all those responsible will be inevitably punished.
"FC Shakhtar calls upon everyone to observe a truce in reality. We require all parties to the confrontation to abandon escalating it and begin peace talks. Stop destroying our city! People and history will not forgive you."