The Manchester City striker Sergio Aguero had earlier scored to put his side 2-0 up, becoming the Albiceleste's third-highest scorer in the process.
But he suffered health issues at the break and was forced to leave the Stadion FK in Krasnodar to be given medical attention.
"He fainted and was therefore transferred to carry out routine checks just as a precaution," said Argentina's official Twitter said.
Aguero underwent tests in hospital as Nigeria came back to record a famous 4-2 win.
After the match, Argentina boss Jorge Sampaoli said: "Sergio got dizzy and had to leave at half-time."
The Argentine Football Federation then revealed that Agüero was "in the hotel along with the rest of the delegation."
Manchester City's official club website then wrote: "Sergio never lost consciousness, and was taken to hospital for precautionary medical checks.
"He will be assessed by the club's medical team ahead of this weekend's Premier League trip to Leicester City."
Arsenal's Alex Iwobi struck twice for Nigeria, including a stunner as he nutmegged Barcelona's Javier Mascherano before slamming home.
Aguero has eight goals in eight Premier League appearances for City so far this season, and his condition will be of huge concern for boss Pep Guardiola.
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