The 32-year-old has also been issued with a court summons, according to a statement from Brazil's civil police, reports Xinhua.
Even if Lochte is not present at the court hearing, he could be tried and faces a penalty of up to 18 months in jail.
In a statement, Lochte said he was with fellow US swimmers James Feigen, Gunnar Bentz and Jack Conger when their taxi was stopped by thieves posing as police.
The athletes were returning to the Olympic Village after celebrating the end of the swimming competition at the Rio Games, according to Lochte.
But police accuse the swimmers of fabricating the story, claiming the swimmers were in fact confronted by security guards after they vandalized a gas station.
Lochte left Brazil before police were able to question him about the incident.
Bentz and Conger were stopped by federal police from boarding a plane at Rio's international airport on August 17.
Feigen agreed to donate nearly $11,000 to a Brazilian charity to avoid charges.
Lochte has lost several sponsors in the past week, including sportswear manufacturer Speedo. But Pine Bros Softish Throat Drops said it had signed an endorsement deal with the swimmer on Friday.
Lochte has won six Olympic gold medals, including one in Rio for his victory with the US 4x200 metre freestyle relay team.
