Assange's lawyer, Per Samuelson, says he filed a criminal complaint with an affidavit by Assange to police at Stockholm's Arlanda Airport today.
The move comes a day before President Barack Obama's visit to Sweden.
WikiLeaks spokesman Kristinn Hrafnsson said similar complaints would be filed in other countries, including Germany and Denmark, alleging potentially unlawful US intelligence operations against Assange.
The affidavit says the suitcase contained laptops with WikiLeaks material, including evidence of a "war crime" allegedly committed by US troops in Afghanistan. Assange says it disappeared when he travelled from Stockholm to Berlin on September 27, 2010.