Harry Greaves, from Bronygarth near Oswestry, was visiting friends in Peru and planned a lone expedition on a mountain on 7 April.
The 29-year-old has not been in contact since - which his family says is "out of character".
His mother and cousin, who is a Spanish speaker, flew out on Sunday morning in the hope of finding him.
"My cousin who speaks Spanish will be our main contact, coordinating everything that will be happening out there," his sister Ellen Greaves said.
"Police have told us nothing will happen until Monday at the earliest but Harry's friends, who he was staying with in Peru, have organised helicopter and night searches with locals."
Mr Greaves flew to Peru to meet two friends who live in Pisac, near Cusco, on 20 February. He emailed his family twice saying he was enjoying his trip.
On 7 April he told his friends he planned on going on a mountain hike alone in Kinsa Cocha and expected to return by 10 April.
"He's done a number of outdoor trips before," said Miss Greaves.
"We understand he went with provisions - with a tent and food."
The family described Mr Greaves as self-reliant and practical, and added it was "out of character [for him] to be out of touch for so long".
The family of a tourist missing in Peru has flown out to South America to help search for him.