Lochte, Feigen and two other members of the US swimming team said they had been robbed at gunpoint in a taxi in Rio.
But police say their account of when they arrived at the Olympic village does not square with CCTV recordings.
Local media report that Lochte left Brazil before the order was issued.
His Twitter account shows footage of him arriving back in the United States on Monday,
Lochte swam in two events at the Rio Games, winning gold in the 4x200m freestyle relay.
Feigen, who is still believed to be in Brazil, won gold in the 4x100m freestyle relay.
Accounts of what happened to the swimmers have been confusing from the beginning.
Lochte first told US TV network NBC about it but International Olympic Committee spokesman Mark Adams said reports of the robbery were "absolutely not true".
The US Olympic Committee (USOC) later confirmed the swimmers' accounts.
Lochte himself told police that he and team mates James Feigen, Gunnar Bentz and Jack Conger had all attended a party in the French Olympic team's hospitality house on Saturday evening.
He said that during their return drive to the Olympic village, their cab was stopped by men posing as police officers.
One of the men held a gun to his head, Lochte said, and robbed him of his money and personal belongings.
But police investigating the case say they have found no evidence of the robbery.
They also point to "inconsistencies" in the swimmers' accounts.
Lochte and Feigen told police they and their fellow swimmers had returned to the Olympic village at 04:00 local time (08:00 GMT).
But CCTV recordings appear to show the swimmers returning to the Olympic village at 07:00 local time.
They can be seen putting their belongings through a metal detector at the entrance to the village in what appears to be a calm manner.
Police say they have not been able to track down the driver who the swimmers said drove them back to the village.
They also said that Feigen and Lochte gave different accounts of how many men robbed them.
Investigators have requested a search warrant for the rooms the swimmers stayed in with a view to examining Feigen's mobile phone.
They said they wanted to trace the swimmers' whereabouts on Saturday night and Sunday morning.
The US Olympic Committee (USOC) confirmed that Brazilian police had sought the passports and further testimony from Lochte and Feigen.
In a statement the committee said: "The swim team moved out of the village after their competition ended, so we were not able to make the athletes available."
The statement said that USOC "do not make athlete travel plans public and therefore cannot confirm the athletes' current location" but that they would co-operate with the Brazilian authorities.

Phillip Shortman, 27, from Abersychan, Pontypool, has admitted 10 counts of fraud and will be sentenced on Friday.
The charges related to selling a "non-existent" phone and vehicle parts on eBay and another website.
Newport Crown Court heard he has 17 previous convictions for 77 offences, many related to eBay.
In the latest case, Shortman admitted using his five-year-old son's details to sell a bogus Samsung Galaxy S4 mobile phone through the online market place.
He arranged for £480 to be transferred into his wife's account, but failed to deliver the phone.
Shortman then attempted the same con again, being paid £440 for the same phone.
The court was told he then "attached" himself to a website selling Suzuki Jeep parts, calling himself Yuppy Bear.
The Essex police officer who failed to receive the parts he ordered from Shortman helped fraud officers in Cardiff arrest him.
Jeffrey Jones, prosecuting, said the value of his fraud was estimated at £2,065.
Mr Jones told the court Shortman had arrived at court with the sum in cash.
The court heard one of his previous crimes, committed when he was 17, had 80 victims.
He has also been convicted of selling bogus Wales Rugby international tickets, worth £7,000.
Nigel Friar, defending, said much of Shortman's offending "had its basis in immaturity and a lack of understanding of money". He said: "Mr Shortman is finally beginning to grow up."
He told the judge, John Jenkins QC, Shortman was remorseful, and "custody has been imposed on a number of occasions since 2007", adding "some would say that has failed".
A judge in Brazil has issued an order preventing US swimmers Ryan Lochte and James Feigen from leaving the country after police queried their evidence in a robbery case.
[NEXT_CONCEPT]
A prolific eBay conman has been caught again after failing to deliver a car part to a police officer who ordered it from him online.