The complaint was filed 8 August 2013.
This could be a repeat of what happened to George W Bush who had to abort his book promotion tour before entering Switzerland where incarceration awaited him.
"Firstly, it's illegal to conduct war and occupation of foreign countries as he's done in Afghanistan and Iraq", says Olofsson.
"It's forbidden to lock people up without trial as he's done in Guantánamo and other prisons in the world. And then it's not at all uninteresting that it's illegal to monitor and spy on Swedish citizens and citizens of the European Union. These are very serious crimes."
Gunnar Olofsson is chief physician and surgeon at Southern Älvsborg's hospital (SÄS) in Borås Sweden.
He's often heard in the Palestine debate. He filed the complaint yesterday with the police in Stockholm.
He now hopes that the Swedish police will dare summon the US president for questioning, in accordance with international jurisprudence.
Rule of Law
Gunnar Olofsson says that Barack Obama should be treated the same as anyone who comes to Sweden and is subject to a police complaint.
"I'm counting on the fact that I as a Swedish citizen am able to influence the political agenda of my country and that my voice will be heard when I report a crime."
Gunnar Olofsson believes that if the police want, they can pull in the US president for interrogation when he visits Sweden in September.
"The problem is that they'd most likely not want to. But I really hope this police complaint will be taken seriously."
Although it might not be possible to convict and incarcerate a head of state, Obama will lose that protection in 2017 and will thereafter be subject to the same judicial process as his predecessor who in Switzerland risked a war crimes conviction.