Her arrest appears to be the first of its kind since the country's cyber ministry was created last month.
The police search warrant showed that central to its investigation was a post on O'Donovan's Twitter feed referring to a "Goblin" whose wife and step-sons had imported a Rolls-Royce, an apparent reference to Mugabe, though he was not named.
"The reported offensive and insulting tweet does not make any mention of the president's name", ZLHR said in a statement.
She denied the allegations which she called "baseless and malicious" in her caution statement.
The alleged tweet follows online reports that Mugabe's two sons, Robert Jr and Chatunga, have imported at least one luxury vehicle from neighboring South Africa.More news: Constitution Bench of SC commences hearing on Delhi-Centre governance row
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Ms O'Donovan's Twitter account was locked on Friday but a photograph on her home page referred to #ShutdownZimbabwe2016, a series of protests past year that rattled Mr Mugabe's Government and elicited a fierce crackdown on the streets and online.
The outlet describes itself as producing "satirical comedy sensations".
According to the Zimbabwe Lawyers for Human Rights, detectives raided her house in Harare early on Friday morning and confiscated her laptop and other electronic equipment.
Police spokeswoman Charity Charamba said she had no immediate information about the case.
Doug Coltart, a human rights lawyer in Zimbabwean capital of Harare, said that if convicted, O'Donovan could face more than 20 years in prison.
Mugabe's spokesman said last month a new cybersecurity ministry had been formed to clamp down on those who, as he put it, do mischief in cyberspace. The tweet also had a photo illustration of the 93-year-old Zimbabwean President with a catheter.