Chile cut trio from their World Cup squad
Coach Jorge Sampaoli announced his preliminary squad on Tuesday in the knowledge that a total of seven players would end up disappointed before his final selection is confirmed on June 2.
Paredes, 33, appeared at the 2010 World Cup in South Africa and has played for his country 33 times since making his debut in 2006, scoring nine goals in the process.
The attacker was also in sensational form for club side Colo Colo during this year's Clausura stage of the Chilean Primera Division, netting 16 times in 13 games.
Fellow forward Canales had previously only played a total of 18 minutes for his national team, with that appearance coming in heavy 4-0 World Cup qualifier defeat to Uruguay on November 11, 2011.
Like Paredes, 32-year-old Canales has enjoyed a good campaign at club level, scoring 12 times in 20 Primera matches for Union Espanola.
Andia, a 21-year-old centre-back with four caps who found himself linked with Bayer Leverkusen in 2013, will also not be on the team's plane to Brazil.
The Chilean Football Federation released a brief statement on Saturday thanking the players on behalf of the team's coaching staff for their "commitment" since earning their initial call-ups.
Chile's Group B campaign gets underway against Australia on June 13, before matches against reigning champions Spain and 2010 runners-up the Netherlands.