The 26-year-old man was located after police appealed for public help to find the animal - for which they have grave health concerns.
Queensland Police were told the mammal had been released in a nearby river but haven't been able to locate it.
The man could face a fine of up to A$430,000 (£231,700, $288,500).
A woman who was with him has also spoken to police.
Surveillance cameras on Tuesday captured the pair boarding a train at Morayfield, about an hour north of Brisbane, holding the animal wrapped in a towel.
"According to the report that was provided to [authorities], they were showing it off to people on the train, allowing people to pat it," Queensland Police's Scott Knowles said.
Police will also allege in court that the pair were seen showing the animal to members of the public at a nearby shopping centre.
Queensland's environment department had stressed that the platypus was at risk of sickness or death the longer it remained out of its habitat, and urged the pair to take it to a vet.
Police said they were advised the platypus had been released into the Caboolture River, but said they were unsure of its condition.
In a statement, police said it was risky behaviour for both the humans and the animal.
"Taking a platypus from the wild is not only illegal, but it can be dangerous for both the displaced animal and the person involved if the platypus is male as they have venomous spurs," it said.
"If you are lucky enough to see a platypus in the wild, keep your distance. Never pat, hold or take an animal."
The arrested man has been charged with taking an animal classified as protected from the wild and keeping a protected animal captive. He will face court on 8 April.
Famously shy and elusive, platypuses are found in eastern Australia, in freshwater creeks, slow-moving rivers, lakes and dams.
The animals are one of only two types of monotremes - mammals that lay eggs - in the world.