Aged 93, Mugabe is the only leader the southern African country has known since independence in 1980, and his health is a hot topic ahead of a presidential election scheduled for next year that he is due to contest.
He flew to Singapore late on Monday. The Ministry of Information said he was expected to return home at the weekend.
Mugabe now struggles to walk, with security aides forming a human shield around him in public, often making it difficult for reporters to film or take pictures of him.
Last week at a World Economic Forum Summit in South Africa, Mugabe sat slumped in his chair, wringing his hands, as he told a panel discussion in a low murmur that his country was not a "fragile state".
Critics say his infirmities make him unfit to hold office but he continues to exercise tight control over his ZANU-PF party. In February he said the party and Zimbabwe's people saw no viable alternative candidate to him for next year's elections.