The 23-year-old should play in the quarter-final.
Messi, 23, was sent back to bed by coach Diego Maradona to recover after turning up with the condition.
An official from the Argentine Football Association said: "He did not train today. He came to the training grounds with a cold, but no fever."
Speaking to Clarin.com, team doctor Donato Villani added: "Messi has flu-like symptoms but nothing serious and it was decided he should not practice. Tomorrow, he will be required to rest."
The Barcelona star, who has yet to score in the World Cup finals in South Africa, is expected to recover in time for Saturday's quarter-final clash with Germany at the Green Point Stadium in Cape Town.
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