The Barcelona superstar and several of his team-mates took ill due to the turbulence during the journey to the city near the Andes where Argentina will face Colombia.
The bout of illness will not stop Messi or any of his colleagues from playing in what is a crucial game for Argentina's hopes of reaching the 2018 World Cup in Russia.
Edgardo Bauza's side are sixth in the South American qualifying group after 11 matches following a 3-0 defeat in Brazil last week.