Ncube had in an interview accused Mugabe of starving opposition supporters and using food aid as a weapon to buy votes ahead of Thursday's parliamentary elections.
"He wants to cause the break-up of the unity of our country," said Labour Minister Paul Mangwana. "He is against the peace and stability that is prevailing in our country.
"I am not sure that he is still a man of God right now," the minister added.
Ruling Zanu-PF spokesman Nathan Shamuyarira blasted Ncube, saying: "He is a mad, inveterate liar. He has been lying from the past two years. As an archbishop, we expect him to tell the truth."
The archbishop has been a thorn in Mugabe's side over the past years, attacking the president's record on human rights and openly supporting the opposition in its bid to come to power.
In an interview with a South African broadcaster, Ncube wished for Mugabe's demise.
"If the Lord did take him away there would be a chance that people will live peacefully because as long as he is around, his cabinet ministers are so afraid, that there will be no change," he said.
Zimbabwe's opposition Movement for Democratic Change and civic groups have said Mugabe's party is using food to buy votes in Thursday's elections, demanding that people show their Zanu-PF cards to get food handouts.
But the government has denied such allegations, with Mugabe promising the people of Bulawayo last week that all hungry people will get food.