The National Criminal Police International Police Cooperation Division (Rikskriminalens enhet för internationellt polissamarbete - IPO) confirmed receipt of the request on Friday.
"We have quality-assured it and it is now being translated into English. It will go out this afternoon," said police superintendent Tommy Kangas Vieri to the TT news agency.
A remand order was issued for Assange on Thursday by Stockholm District Court on probable cause suspected of rape, sexual molestation and unlawful coercion.
Julian Assange did not attend the remand hearing and as a result of the court's decision to detain Mr. Assange in his absence, an international arrest warrant was the next step in the legal process, the prosecutor's office said in a statement.
Assange's Swedish lawyer Björn Hurtig has called the prosecutor's petition "exaggerated" and "out of proportion", claiming that his client had made several offers to submit himself to police questioning.
Prosecutor Marianne Ny however said on Thursday that she was not aware of these offers, explaining that "the district court shared our opinion that there is flight risk in this case".
An international arrest warrant is published in three law enforcement systems - the Swedish, the Schengen system SIS and Interpol.
When asked how long it usually takes for a wanted person to be detained, Kangasvieri said:
"It can proceed quite fast."
There are three routine ways for police to apprehend a suspect. The simplest is to visit a registered address and make an arrest. Many are detained in traffic checks and can be detained on the spot.
"If they try to leave the country by air then the system reacts when their passport is checked," said Kangasvieri.
Assange's UK-based lawyer Mark Stephens said his client plans to challenge the district court order for his arrest in the appeals court.
The 39-year-old whistle blower has admitted that he had met both women at the centre of the case, who according to their lawyer are both Swedish and aged between 25 and 35, saying "they were both at my press conference."
He has since insisted that he has never had non-consensual sex with anyone, and refused to discuss whether he had sexual relations with the women in question, saying it was a "private matter".
Assange has repeatedly denied committing any crime and has criticised how Swedish prosecutors have handled his case, claiming that he plans to sue for damages.
WikiLeaks last month published 400,000 classified US documents on the Iraq war. It enraged US authorities by posting 77,000 secret US files on the Afghan conflict in July.