The family of Mr McConkey, now 19, say he was left "traumatised" after "degrading" videos were recorded of him on the trip in December 2022.
A PSNI spokesperson said: "Police received a report on January 24th 2023 of videos being circulated amongst members of the school population.
"Neighbourhood officers liaised with the school and appropriate guidance and support was provided. An investigation was conducted following receipt of this report.
"No further police action was taken."
Speaking on Good Morning Ulster, the education minister said it is "unacceptable that this occurred".
Paul Givan also described it as a "terrible incident" and said it's "been a very sorry state of affairs".
"We will seek reassurances in incidents like this, from any school involved, that the appropriate measures are being put in place so that there isn't a repeat of this," Givan added.
Givan added that he has "no doubt" that the school takes this seriously.
The IRFU is the governing body for rugby on the island of Ireland, covering the four provinces, including Ulster.
A spokesperson said: "The IRFU was made aware of an alleged incident on a school trip abroad. As this was not an IRFU event, we signposted to the relevant authorities for investigation."
Methodist College said it contacted police and that disciplinary action was taken but did not elaborate on the details.
A spokesperson for the school said: "A claim for compensation was brought by Mr McConkey and was settled with the school's insurers.
"The fact that these incidents occurred during downtime following training sessions and during sleeping hours has caused the school to review and improve its supervision procedures.
"Updated supervision procedures have been in place in the two years since these incidents occurred and to the school's knowledge there has been no recurrence of any such incidents."
The person in charge of the 2022 trip is still involved in rugby at the school.