Mr. Mugabe, who served as Zimbabwe’s leader for 37 years, was forced to step down in late November after the military seized power and put him under house arrest.
His successor, President Emmerson Mnangagwa, has emphasized his desire to repair relations with Western governments, whose support will be crucial in obtaining assistance from international creditors. Local and international rights groups had pressed for Ms. O’Donovan’s release.
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The government, could revive its effort to put Ms. O’Donovan on trial by presenting new evidence, but Linda Gatsikwa, a prosecutor, gave no indication of what the state would do.
Ms. O’Donovan, of Martinsville, N.J., and a 2014 graduate of the Gallatin School of Individualized Study at New York University, smiled and hugged friends after the court appearance but made no comment.
Her arrest, which came less than two weeks before Mr. Mugabe’s resignation, had raised fears that the Zimbabwean government was stepping up efforts to control social media before national elections scheduled for mid-2018.
The Zimbabwean government, which had established a cybersecurity ministry a month before her arrest, began cracking down on social media in 2016 after activists using WhatsApp and Facebook organized street protests against Mr. Mugabe’s government.
In November, prosecutors said that Ms. O’Donovan had “systematically sought to incite political unrest through the expansion, development and use of a sophisticated network of social media platforms as well as running some Twitter accounts.”
Prosecutors said that she had access to the anonymous account that had posted the offensive tweet, which included a photograph of Mr. Mugabe, 93, with an illustration of a catheter, but they presented little evidence to support their accusation that she was responsible.