Hours earlier, the head of the armed forces, General Constantino Chiwenga, has demanded an end to a purge in the ruling Zanu-PF party.
Overnight, at least three explosions were heard in the capital, Harare, and military vehicles were seen in the streets. "We want to pacify a degenerating political social and economic situation in our country".
The streets of Zimbabwe's capital Harare were eerily quiet on Wednesday morning but wartime songs were broadcast over state radio and TV stations, while soldiers stopped pedestrians and motorists to ask for identity documents, witnesses say.
The US State Department said it was "closely monitoring" the situation in Zimbabwe and urged all parties to resolve disputes "calmly and peacefully".
The military added that Mugabe and his family were "safe and sound and their security is guaranteed".
He warned against targeting "members of the party with a liberation background" - a reference to Zimbabwe's struggle against white minority rule in the 1970s.
Soldiers are reported to have taken over the headquarters of Zimbabwe's national broadcaster ZBC, amid a growing political crisis.
Despite an often abrasive manner, Grace Mugabe's commanding presence and charity work have won support from some Zimbabweans.
Zanu-PF said Gen Chiwenga's stance was "clearly calculated to disturb national peace. and suggests treasonable conduct on his part as this was meant to incite insurrection".
Neither the president nor his wife responded in public to the general's remarks and state media did not publish Chiwenga's statement.
Mnangagwa, 75, was widely viewed as Mugabe's most loyal lieutenant, having worked alongside him for decades.
Mnangagwa, who enjoyed the backing of the military and is known as the "crocodile" because of his perceived shrewdness, fled the country.
Both the United States and British embassies in Zimbabwe have advised their nationals to stay indoors because of what they call the 'uncertain situation'.
"Defending the revolution and our leader and president is an ideal we live for and if need be it is a principle we are prepared to die for", Kudzai Chipanga, who leads the ZANU-PF Youth League, said at the party's headquarters in Harare.
Soldiers stand beside military vehicles just outside Harare, Zimbabwe Nov. 14, 2017.
The South African cites reports that Robert Mugabe has actually been under house arrest for the last few days - a claim denied by Zanu-PF's official Twitter, which insists there is "NO coup happening".
"Let it be clear that we intend to address the human security threats in our country".
The Army last night announced that they had taken over government business, with the intension of dealing with President Mugabe's ministers who were misleading the aged leader.