The privately owned Standard newspaper quoted "impeccable" sources as saying that Grace "slipped and fell in the bathroom at (the Mugabes’) Borrowdale house and is suspected to have suffered a dislocated hip".
George Charamba, Mugabe’s spokesman, confirmed the Mugabes had gone to Singapore, but told the state-run Sunday Mail it was "a straightforward visit".
Charamba would not confirm that the first lady had gone for medical reasons, but told The Standard Grace had not fully recovered from a complication she suffered 14 years ago while giving birth to her youngest son.
"What I know is that the first lady, after the birth of Chatunga, developed some some slight discomfort with her back, but that was a long time ago," he said.
"However, it could not be anything serious," he added, referring to her trip.
Charamba told the Sunday Mail in a statement that the Mugabes were expected home Sunday.
"It is a straightforward visit. It cannot be anything more than that," he said.
In February and March Mugabe flew to Singapore for eye check-ups following a cataract operation there.
Mugabe married Grace in 1996 following the death of his first wife, Sally, in 1992.
Mugabe and Grace have three children together.