Heavy gunfire and artillery were heard in northern suburbs of the capital, Harare, early on Wednesday.
Zimbabwe's envoy to South Africa, Isaac Moyo, earlier dismissed talk of a coup, saying the government was "intact".
The statement read out by Maj Gen Sibusiso Moyo came hours after soldiers overran the headquarters of ZBC. He 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.
|Zimbabwe crisis: Army seizes broadcaster but denies coup|
- Citizens should remain calm and limit unnecessary movement
- The military assures the Zimbabwean judiciary that its independence is guaranteed
- Security services should "co-operate for the good of our country" and any provocation would "be met with an appropriate response"
- All leave for the defence forces is cancelled and personnel should return to barracks immediately
|Tweet from US Embassy Harare|
Gen Chiwenga said the army was prepared to act to end purges within Mr. Mugabe's Zanu-PF party.
|Image: AFP Image caption Zimbabwe Army General Constantino Chiwenga warned of a military takeover|
|President Robert Gabriel Mugabe speaking with the press|