"He was freed for medical reasons after three and a half years' detention," Fanak Mani, the daughter of Massud Mossaheb, told AFP.
Mr Mossaheb is being held at Evin prison, near the capital Tehran.
A photo posted on the Free Massud Twitter account shows him smiling, supporting himself on a crutch, with his wife by his side.
Mr Mossaheb was the general secretary of the Austro-Iranian Society, an organisation that encourages exchanges between the two countries.
He was arrested in Tehran in January 2019 while he was accompanying a visiting group of Austrian scientists.
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Mr Mossaheb's family has on several occasions raised concerns about the state of his health.
More than 10 dual-nationality Iranians from western countries are being held by the authorities in the country.
Rights groups such as Amnesty International have condemned their detention as "hostage-taking" for political ends, as a means to put pressure on western powers to win concessions.
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Iran, which does not recognise dual nationality, says that all of the people held have been detained after rulings by the courts.