The player's agent told Reuters that the warrant was no longer in force and Valencia would travel to play for his country against Bolivia in La Paz on Tuesday.
The striker, on loan at Premier League Everton from West Ham United, was being pursued over unpaid alimony to his ex-wife, according to local media reports.
Ecuadorian police gathered at the door of the team coach before the World Cup qualifier against Chile and then waited by the pitch to apprehend him after the game.
In a bizarre incident, the player appeared to be chased by officers while being transported on a medical buggy having been substituted after receiving on-field treatment for altitude sickness with 10 minutes remaining.
“It’s been made public that the arrest warrant has been revoked," his agent Gonzalo Vargas told Reuters.
“He still has to be notified and it’s a documentation matter that the lawyers are dealing with but obviously he can travel. It’s a process that could take some hours and he is joining the national team squad today.”
Vargas refused to say why the warrant had been revoked or answer further questions.
Valencia owes $17,000 (£13,651) to his former partner, according to media reports.
The 26-year-old moved to the Premier League to join West Ham from Mexican side Pachuca in 2014. He signed for Everton on loan after two full seasons at the East London club in which he scored four Premier League goals in each.
Ecuador are in third place in the 10-team South American World Cup qualifying group. The top four qualify automatically for Russia 2018 and the fifth-place side goes into an intercontinental playoff with a team from Oceania.
(Writing by Andrew Downie; Editing by Toby Davis)
