Chilean football governing body ANFP accepted a request by national team players on Wednesday to call off the match because of ongoing violence in the South American country, reports Xinhua news agency.
A scheduled friendly against Bolivia in Santiago this week had already been suspended due to security concerns.
"The players arrived with great disposition, they met and the decision was made not to travel to Peru, considering that it is the best show of solidarity. It's something that is very respectable," Rueda told reporters late on Wednesday.
"I came (to the job) to work in football and if this continues, ... if there is no football, I have to go. It is unusual, it is not normal. The question is, when is the situation going to be normalized."
Rueda has led the Roja to seven wins, seven draws and eight losses since taking charge of the team in January 2018. The 62-year-old Colombian had said the friendlies against Bolivia and Peru would allow him to test his players for the last time before the South American zone's 2022 World Cup qualifiers begin next March.
Chile has been gripped by unrest since October 20, when protests against a now-suspended hike in subway fares in capital Santiago morphed into a wider movement demanding lower living costs and greater income equality.
At least 20 people have been killed and hundreds more injured amid clashes between protesters and police, looting and arson attacks, according to local authorities.
( With inputs from IANS )