Both players arrived at Frances Clairefontaine training base on Monday morning.
But after being assessed by Frances team doctor Franck Le Gall, Pogba and Martial have both been released and will play no part in Frances upcoming fixtures.
The world champions will face Netherlands in their Nations League group game on Friday evening before playing Uruguay in a friendly next Tuesday.
Pogba missed Manchester Uniteds 3-1 defeat to Manchester City at the Etihad Stadium on Sunday due to a thigh strain.
Martial, meanwhile, played the full 90 minutes and scored Uniteds penalty after Romelu Lukaku was brought down by Ederson.
Pogba and Martial have been replaced by Tottenham midfielder Moussa Sissoko and Arsenal striker Alexandre Lacazette.
When asked about Pogbas injury, Jose Mourinho said before Uniteds loss to City: Paul is injured. He was injured during the game in Turin. He resisted.
He felt that he could resist. He felt that was such a crucial match for the team.
He made that sacrifice for us, and then it was impossible for him to recover for this match.
More: Manchester United FC