Sources close to the president's camp say he is livid about the claims that Mrs Mugabe, who is 41 years his junior, had a five-year affair with Gideon Gono, one of his closest friends and the head of Zimbabwe's Reserve Bank.
The 86-year-old leader is due to convene an emergency meeting with senior aides and Dr Gono today and could take legal action to silence the rumours.
Mr Mugabe's spokesman denied suggestions that Dr Gono had gone into hiding amid fears his life might be in danger.
Meanwhile Grace Mugabe is said to be "extremely upset" and lying low at the family's £4m mansion in Hong Kong, where their daughter Bona attends university.
She and married Dr Gono were alleged to have met up to three times a month at her farm, friends' houses or at hotels in South Africa and Malaysia, and to have intended to set up home together after Mr Mugabe died.
He was said to have been "devastated" when he learned of the allegations from his sister Sabina, shortly before she died three months ago.
A man previously alleged to have had an affair with his wife, Peter Pamire, died in mysterious circumstances and another, businessman James Makamba, fled to the UK apparently fearing the same fate.
Robert and Grace Mugabe, a former typist in his office, began their affair when he was still married to his terminally ill wife Sally, and married in 1996.
Dr Gono could not be reached for comment although staff in his office insisted he had turned up for work "as normal".
A source said to be close to the Mugabes and Dr Gono told the website New Zimbabwe said they were planning a joint fightback.
"There is a major meeting planned for Wednesday which will be attended by lawyers and advisers to the President and Gono," she said.
Another source said: "Dr Gono is a very trusted individual who had been allowed more than any other person access to the family.
"Gideon Gono needs to get this sorted and needs to clear this very fast to restore the trust of the president."
