The field was in bad shape on Sunday, when Argentina defeated Qatar 2-0, with dry patches visible along the sidelines and areas where the turf was completely gone, reports Efe news.
Messi ripped the Arena do Gremio, saying that the field was in terrible condition.
The superstar striker told the press that all the fields on which Argentina had competed in the Copa America "are very bad", making it hard to control the ball when taking a shot on goal.
The stadium's management, following tournament rules, did not allow Brazil or Paraguay to practice at Arena do Gremio ahead of Thursday's quarterfinals match.
The policy was put in place by Copa America organisers to prevent wearing down the turf ahead of a match.
As was the case before previous matches, the teams were not allowed to take the field at Arena do Gremio before playing their match.
Venezuela, however, were able to practice at Arena do Gremio on the eve of its match with Peru, the first of five Copa America contests played in Porto Alegre.
Brazil will not only have an edge as host, but forward Everton, who plays for Gremio, will be in action on his home field against Paraguay.
Brazilian national soccer team coach Adenor Leonardo Bacchi, better known as "Tite," and assistant coach Edu Gaspar had a walk-through at the stadium on Monday to get a first-hand look at field conditions.
Coach Tite's squad has improved its level of play on the field and is heading into the clash with Paraguay at Arena do Gremio in Porto Alegre fresh off a 5-0 blowout of Peru in its last match in the group phase.
Brazil, however, will have to win without midfielder Casemiro, who will miss Thursday's quarterfinals match due to an accumulation of yellow cards.
Paraguay have been a tough opponent, knocking off Brazil the last two times the squads met in the knockout phase of the Copa America - in Argentina in 2011 and Chile in 2015.
( With inputs from IANS )