Editor of independent newspaper NewsDay Wisdom Mudzungairi and journalist Richard Chidza were released ahead of a court appearance tomorrow.
The front-page story said that Mugabe, 93, had "sneaked out of the country" this week, and quoted an unnamed source saying "it's a tricky health situation".
The report, headlined "Mugabe in fresh health scare", said that first lady Grace Mugabe had flown to Dubai to organise the charter flight.
He said their arrest was "in relation to the paper's lead story".
Mugabe's trip to Singapore, shortly after his lavish 93rd birthday party, was announced by his press spokesman on Wednesday.
The president is expected to return early next week.
Mugabe's health has been subject of increased speculation in recent years, and he regularly flies to Singapore for medical attention.
Despite his advanced age, Mugabe's ruling ZANU-PF party last year endorsed him as its candidate for the 2018 general elections.
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