The court ruled 5-2 that the warrant for his arrest was properly issued. Should she decide to contest, Assange's attorney has two weeks to file a challenge to Wednesday's ruling.
Assange is facing sex crimes allegations in that country but has not been charged. Claims by two women that Assange sexually assaulted them emerged around the same time he posted classified U.S. military and diplomatic cables.
Assange claims Sweden fabricated the arrest warrant in retaliation. For now, Assange is due to be sent back to Sweden next month.
The Associated Press contributed to this report.