It said it took action to “target criminals”.
However, it said this was not “a military takeover of government” and that President Robert Mugabe was safe.
Zimbabwe’s envoy to South Africa, Isaac Moyo, earlier dismissed talk of a coup, saying the government was “intact”.
The statement read out by the military came hours after soldiers overran the headquarters of ZBC.
An officer in uniform said: “We wish to assure the nation that his excellency the president… and his family are safe and sound and their security is guaranteed.”
The statement added: “We are only targeting criminals around him who are committing crimes… that are causing social and economic suffering in the country. As soon as we have accomplished our mission, we expect that the situation will return to normalcy.”
The statement did not name those targeted but a government source quoted by Reuters said finance minister Ignatius Chombo was among those detained.
It is not clear who is leading the military action.
The UK Foreign Office advised Britons “currently in Harare to remain safely at home or in their accommodation until the situation becomes clearer”.
It also advised US citizens in Zimbabwe to “shelter in place” until further notice.