The Swede is among around 100 people who have been arrested in 19 different countries and the US authorities have sought his extradition, according to a report in the Dagens Nyheter (DN) daily on Tuesday.
The man is reported to have been under house arrest in Chisinau, Moldavia since November and is receiving assistance from Swedish embassy.
"The USA has applied for his extradition, but that is a matter for Moldavia and the USA," said Karin Nylund at the Swedish Foreign Ministry to DN.
The case involves the disbursement of the Blackshades software programme which enables the hijacking of computers which can then be remotely controlled and monitored. The programme is not in itself illegal but can be used for illegal activities.
The FBI estimates that Blackshades has been used to take over some 500,000 computers in the 19 countries in question.
The programme retails for $40-100 and according to the FBI, sales have generated some 2.3 million kronor ($350,000) to date for the Stockholm-based Swede who has been identified as the creator and owner of the programme.
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The software made headlines in the US in September 2013 after it was used to take naked pictures of Miss Teen USA.
According to the DN report the FBI trail led back to the Swede following information divulged by a 23-year-old American colleague who was arrested in 2012.