Melissa Reid, from Lenzie in East Dunbartonshire, and Michaella McCollum Connolly, from Dungannon in Northern Ireland, were given Easter eggs and a KFC takeaway by Paul Higgins, who saw them while he was touring with the chart-topping band.
The pair were arrested last August after being caught in possession of £1.5 million worth of cocaine at Lima International Airport.
They claimed they were forced to travel to Peru to smuggle 11kg of the class-A drug out of the country.
After a trial in December, they were sentenced to eight years in prison.
Both had their terms reduced to six years and eight months after entering guilty pleas and Reid has submitted a prisoner transfer request to allow her to serve the rest of her sentence in Scotland.
Mr Higgins is understood to do charity work and a source said he believed it would be the "Christian" thing to visit the girls while he was nearby.
Melissa Reid's father, Billy Reid, said it was "great" of Mr Higgins to visit the pair.
"Obviously the band themselves wouldn't have been able to go to prison but it's really nice that Paul Higgins went to see the girls," he said.
"It will really lift their spirits to get to meet and speak to the manager of such a massive band. They do get visitors but no-one like this. "I think it will have helped the girls to hear how One Direction cope with fame because since everything has happened they've been pushed into the spotlight but obviously for different reasons."