The keeper cut the ball out with his foot and the French forward tumbled to the ground, knocking his right shoulder.
During Brazil's 1-0 victory over Cameroon on Tuesday, Neymar was forced off the field after just eight minutes, while Mbappe was substituted in the first half of France's 1-0 win against Uruguay after falling awkwardly on the pitch.
According to The Evening Standard, the Ligue 1 club have offered a statement claiming that the pair will undergo treatment over the next two days before any further updates.
Paris St Germain said on Wednesday that Neymar had suffered a groin strain and Kylian Mbappe a bruised shoulder while on worldwide duty, a week ahead of a crucial Champions League clash against Liverpool.
The club revealed that Neymar has suffered a groin strain, whilst Mbappe has been diagnosed with a bruised right shoulder.
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Neymar played down his injury, saying in an Instagram message that "it was nothing serious".
PSG star Neymar is out of the Champions League match against Liverpool, La Gazzetta dello Sport reported.
Asked whether the Brazil global would be available against Toulouse and Liverpool, Lasmar said: "It's important to wait approximately 24 hours more".
France coach Didier Deschamps said Mbappe, the 19-year-old forward who shot to global prominence at the World Cup, "had some shoulder pain after his fall". "He felt a discomfort, he will need a bit more time to evaluate it and take a scan, but in principle it is not a serious injury".
Neymar's replacement in the Brazilian lineup, Everton's Richarlison, headed in on the stroke of half-time to secure victory for the Selecao.
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