Finance Minister Ignatius Chombo has reportedly been detained by the military along with the chairman of Zanu PF's youth league while other ministers on the wanted list are said to be on the run.
Heavy gunfire was heard in the capital as the military announced a takeover of power early Wednesday morning but denied staging a coup.
A spokesman said President Robert Mugabe and his family were safe and that their security was guaranteed.
The veteran leader has not been heard from or seen and the army did not disclose his where he was being held.
"We are only targeting criminals around him (Mugabe) who are committing crimes that are causing social and economic suffering in the country in order to bring them to justice," Major General SB Moyo, Chief of Staff Logistics, said on television.
"As soon as we have accomplished our mission, we expect that the situation will return to normalcy."
A government source has confirmed that finance minister Ignatius Chombo was taken into detention after three of his guards were shot dead at his home.
The official said military police arrived at Chombo's home in the capital and his body guards opened fire before they were shot at.
Zanu PF Kudzai Chipanga was also said to have been detained. On Tuesday Chipanga held a press conference denouncing defence forces commander General Constantine Chiwenga.
A number of other cabinet ministers were said to be on the run with the whereabouts of the likes of vice president Phekezelela Mphoko unknown.
Meanwhile, it was business as usual in the capital as people went about doing their business with shops and banks open.
However, strategic places such as State residences and offices remain heavily manned by soldiers including Parliament and the Zanu PF headquarters.