He described Mugabe as a "giant African tree that has fallen".
He died in a Singapore hospital a week ago.
Mnangagwa's emissaries, in negotiations with the family, threatened to seize various properties from the former president's widow and children in a dramatic showdown that ended in surrender by the family.
Some of Mugabe's relatives have expressed bitterness at the way former close associates, including Mnangagwa, overthrew him after 37 years in power amid mass protests against his rule.
"For his own peace of mind, he made a decision to leave the country", said Zhuwao.
Mugabe's burial will be delayed for at least a month, because the Mugabe family and the government have been negotiating how and when the leader will be laid to rest.
The threats were reportedly issued in a meeting with the Mugabe family and the government represented by Ziyambi Ziyambi, Philip Chiyangwa and Gideon Gono.
Zhuwao and Kasukuwere - along with Jonathan Moyo, Walter Mzembi, Mandi Chimene and Godfrey Gandawa - are some of the former ministers who were part of Mugabe's inner circle and have since fled the country. Asked if the former First Lady was planning to go into exile, Robert Mugabe's nephew Leo Mugabe said: "She is Zimbabwean, she has no reason to go anywhere".
The Former President'ss burial arrangements have been marred by twists and turns with different family members giving conflicting statements.
We owe an enormous debt of gratitude to Grace for caring for the former president.
A state funeral service attended by almost two dozen current and former heads of state was held in Harare on Saturday, but Mugabe is not expected to be buried until at least next month after the family - having lost in its push to bury him away from the shrine - insisted on a mausoleum being constructed as a compromise.
According to Osinbajo, the passing on of Mugabe is indeed sad, especially for those who are leaders today.
When Mugabe came to power in 1980, his country had high hopes for him and the newly-independent Zimbabwe. Mrs Mugabe had to train staff to assist the family. He was looked after by domestic workers who had no medical training; these are the people who were assisting Mrs Mugabe to look after her husband.
"When he needed to go on regular trips to see the doctor, they had to order the equivalent of Uber, called Grab - a Singaporean transport company offering this service", said Zhuwao. Family members and political leaders head the procession of Mugabe's casket.
Zhuwao repeated his assertion that the treatment Mugabe received had alienated him from his country of birth, for which he had fought.
Plus, the country has other pressing concerns: Zimbabwe's economy is suffering. Mugabe actually oversaw the monument's construction: Heroes' Acre was built as a special burying place for top officials of the ruling ZANU-PF party who helped to end minority white rule.
"Zimbabwe will forever cherish the overwhelming show of sympathy from our brothers and sisters at this moment of grief and their acknowledgment of the sacrifices of the late Cde Mugabe in dismantling colonialism in its various manifestations, not only in Zimbabwe but beyond". The man who lies before us was for years our leader, our commander, mentor and President, both in the party and Government. Mr Mugabe said ZANU-PF owned the land on which the two houses were constructed. "He even said, leading up to our elections, that he would be voting for Chamisa".