The former vice president was also expelled from Zanu PF, a party he served for more then 40 years, a lot of them at Mr Mugabe's side.
The speech came a day after Mugabe publicly criticised Mnangagwa for the first time during a speech at a rally on November 4.
Mnangagwa - whose nickname is the "Crocodile" - defiantly told Mugabe that the party was "not personal property for you and your wife to do as you please".
"The current purging and cleansing process in ZANU-PF which so far is targeting mostly members associated with our liberation history is a serious cause for concern for us in the defence forces", said Chiwenga, at a press conference, reading from his statement.
"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.
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But the 75-year-old former vice president has powerful military connections, having served as defence and state security minister. Grace Mugabe, 52, did not fight in that war.
Martha O' Donavan, in black hood, the American woman charged with subversion over allegedly insulting President Robert Mugabe on Twitter, gets into an American Embassy vehicle after presenting herself to prison officers at Chikurubi Maximum Prison on the outskirts of Harare, Friday, Nov. 10, 2017.
Chiwenga urged unfettered participation at the party's December special congress to choose new leaders.
He called for the expulsion of "the known counter-revolutionary elements who have fomented the current instability in the party".
Mnangagwa was subsequently fired from the party and has since left the country.
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The army boss said the infighting in the party had impacted the country, which is reeling under an economic crisis.
He said the ZANU-PF had been undermined by "gossiping, backbiting and public chastisement" since 2015, and added, "Indeed, the party is undoing its legacy built over the years".
Among other security threats emanating from the goings-on Zanu-PF were "reckless utterances" by some politicians denigrating the military, which he said were causing despondency among its members, he said.
Zimbabwe in 2009 abandoned its own currency in favour of the United States dollar due to hyperinflation.
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