His body was found by a man on a morning hike in Platteklip Gorge on Sunday, said Captain FC van Wyk.
He immediately informed rescue and police services.
The 19-year-old was reported missing at 22:47 on Saturday, said Western Cape health emergency medical services spokesperson Robert Daniels.
He said he was informed that the teen was a tourist from Iceland.
"We are unable to speculate as to his cause of death."
Van Wyk said his next of kin had yet to be informed.
A post-mortem would determine the exact cause of death.