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.
Earlier, BBC correspondents in the capital, Harare, reported that a few armoured vehicles had been seen on a main public road outside the city having left one of the country's main military barracks, Inkomo.
It is not clear where they were heading but they were not seen on the streets of Harare. One of the vehicles had broken down on the side of the road.
Gen Chiwenga's warning of possible military intervention came on Monday at a news conference at the army's headquarters.
He said the "purging" within Zanu-PF was "clearly targeting members of the party with a liberation background", referring to the country's struggle for independence.
"We must remind those behind the current treacherous shenanigans that when it comes to matters of protecting our revolution, the military will not hesitate to step in," he said.
Mr Mnangagwa is one such veteran of the 1970s war which led to independence.
Gen Chiwenga gave his address surrounded by 30 senior army officers.
But the leader of Zanu-PF's youth wing, Kudzai Chipanga, said the general did not have the full support of the entire military.
"We will not sit and fold hands while threats are made against a legitimately-elected government," he warned.
The youth wing supports President Mugabe's wife, Grace, as his successor - something which the former vice president had opposed.
Mr Mnangagwa had told Mr Mugabe that Zanu-PF is "not personal property for you and your wife to do as you please" before he was forced into exile.
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