Harry Greaves, from Bronygarth near Oswestry, was visiting friends in South America and planned to hike a mountain alone on 7 April.
The 29-year-old has not been in contact since - which his family says is "out of character".
They are planning to fly there after a search of the area failed to leave any indication of his whereabouts.
Mr Greaves flew to Peru to meet friends 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 expedition in Kinsa Cocha alone and expected to return by 10 April.
"He's done a number of outdoor trips before," his sister Ellen Greaves said.
"We understand he went with provisions - with a tent and food."
"We've contacted the Foreign Office here. Interpol now know all the details. And out there his friends have contacted the local police, local bus stations, local taxis," Miss Greaves added.
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".

Among those detained is his brother-in-law and one of the two pilots who flew Guzman to his home state.
Mexico's attorney general said a member of Guzman's legal team, described as the mastermind, was also arrested.
Guzman, head of the Sinaloa cartel, escaped from a high-security prison through a specially dug tunnel.
Attorney General Arely Gomez told reporters on Wednesday that the suspected mastermind of the escape had repeatedly entered Altiplano prison to visit Guzman and update him on the operation's progress.
She also said Guzman's brother-in-law had supervised the construction of the mile-long escape tunnel and organised transport.
"Today we are able to affirm that the group responsible for planning, organising and carrying out the escape from outside the prison has been broken up,"  Ms Gomez said, without naming the suspects.
The development comes days after officials revealed the drugs lord had suffered face and leg injuries when he narrowly evaded a police operation to recapture him in north-west Mexico earlier this month.
Ms Gomez confirmed on Wednesday that after his escape, Guzman travelled by land to the city of Queretaro, from where he caught a small plane to his home state of Sinaloa.
His escape was an embarrassment for Mexican President Enrique Pena Nieto, who Guzman taunted on Twitter after the event.
Several prison officials have already been arrested under suspicion of giving inside help to Guzman, who fled through a tunnel that ran 1.5km from under a shower in his cell to outside the prison.
Guzman was first arrested in Guatemala in 1993 and spent nearly a decade in another maximum-security Mexican jail before escaping, reportedly in a laundry basket.
He was on the run for 13 years before being held again in 2014 after a series of high-profile arrests of associates and covert surveillance by the US authorities.
The family of a man feared missing on holiday in Peru say they are growing increasingly concerned.
[NEXT_CONCEPT]
Mexico officials say they have arrested six key people who allegedly helped fugitive drug cartel leader Joaquin Guzman escape from jail in July.