The Brazilian was forced off the pitch with a groin problem during his nation's global friendly against Cameroon at Stadium MK.
Mbappé meanwhile went down as he ran through on Campana in the Uruguay goal, and twisted his arm and shoulder as he landed.
"He has a sore shoulder, he's fallen badly", Deschamps said, according to Sky Sports.
Neymar was withdrawn early for Brazil and Eric Maxim Choupo-Moting hopes his PSG team-mate is not seriously injured.
As it happened for Brazil and France, both secured 1-0 wins over Cameroon and Uruguay respectively, in spite of the injuries to the star duo.
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A statement on the club's official wesbite read: "Neymar Jr and Kylian Mbappe have undergone medical examinations today that confirmed: for Neymar an elongation of the right adductors".
"Thank you to everyone who sent messages wishing me a speedy recovery, I don't think it's serious", Neymar wrote on Instagram.
And Brazil team doctor Rodrigo Lasmar has also suggested Neymar's gorin issue is not a major concern.
For Kylian Mbappe a contusion of the right shoulder.
Neymar was replaced at Stadium MK by Everton's Richarlison, who scored the only goal just before half-time. "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".
While signs are positive for his availability for a potentially make-or-break Champions League match against Liverpool next week, the source said that he is likely to miss PSG's match against Toulouse in Ligue 1 on Saturday.