The Isis fighter, believed to have been called Abu Othman, died after a bombing on an Isis propaganda centre in Anbar Province in Iraq last Friday, Sweden's Svenska Dagbladet newspaper reported on Tuesday.
According to the paper he was involved in broadcasting Isis' extremist messages on an Iraqi radio station.
A total of 23 people are understood to have been killed in the raid in Anbar. But Sweden's Foreign Ministry was unable to give further details on the Swede's apparent death.
"The situation means that it is very difficult to confirm deaths in the conflict zone in Iraq," Gabriel Wernstedt, a press spokesperson for the ministry, told Swedish newswire TT.
Sweden's Security Service, Säpo, does not comment on individual cases but has previously said it has reliable information suggesting that around 150 Swedes are in the region fighting alongside Isis, with a further 50 people known to have returned to Sweden having previously been involved with the radical Islamist group.
Around 40 Swedes have so far been killed fighting for Isis, according to Säpo.
In April, a spokesperson for the security service told The Local
there was "very little" it could do to stop people travelling to Syria and Iraq to join al-Qaeda inspired groups, as EU officials estimated up to 6,000 people from across Europe had fought in the war-torn nation.
"It is completely unacceptable that Swedish citizens are travelling to [join] IS, financing the organization, or fighting for it," Justice Minister Morgan Johansson and Home Affairs Minister Anders Ygeman wrote in a joint article in the Dagens Nyheter newspaper.
"We have a responsibility for what our citizens do both here at home and in other countries," they added.