General Constantino Chiwenga had challenged President Robert Mugabe after he sacked the vice-president.
Gen Chiwenga said the army was prepared to act to end purges within Mr Mugabe's Zanu-PF party.
The party said the general's comments were "calculated to disturb national peace... [and] incite insurrection".
In a statement, the party said it would never succumb to military threats, and that it "reaffirms the primacy of politics over the gun".
Mr Mugabe sacked Vice-President Emmerson Mnangagwa last week, amid a row over the 93-year-old president's successor.