The man was involved in a people-smuggling ring and sent profits to fund terrorism in Syria, according to the Dagens Nyheter (DN) newspaper.
The suspect, who is reportedly in his mid-forties, has lived in Sweden with his family since 2012 and was arrested in Denmark at the Kastrup airport.
He worked for the network from his apartment in Finspång, to the south east of Sweden.
The network, which was based in Italy and busted by an undercover Italian policeman, is said to have sent 20 million kronor to a Syrian jihadist group, the Al-Nusra Front.
The group is fighting the Syrian government and attempting to establish an Islamic state in the country.
The suspect denies the charges.
DN reports that the man had been under investigation by Swedish police in the past. In 2017, police found 700,000 kronor in cash on him and his brother during a traffic control.