Arsenal's Saliba played the full 90 minutes in a 2-0 defeat by Manchester City in Sunday's League Cup final, before the FFF announced his injury.
"The Arsenal centre back is suffering from recurring pain in his left ankle, requiring treatment and a minimum rest period of 10 days," it said in a statement.
"National coach Didier Deschamps has decided to replace him with Maxence Lacroix," the FFF added.
The Crystal Palace defender, 25, has earned his first France call-up, ahead of the 2026 World Cup. He has played 43 games in all competitions this season.
Saliba was among the expanded 27-man France squad announced by Deschamps on Thursday.
France will face Brazil in Boston on March 26 before taking on Colombia in Washington on March 29.
The 2022 World Cup runners-up are in Group I at this year's tournament with Senegal, Norway and a winner from the inter-confederation playoffs.