Saliba, 25, collapsed to the pitch without any contact around the half-hour mark of Tuesday's 2-0 loss and was seen telling team-mates: "My back is gone, my back is gone."
According to L'Equipe, the defender is now set for surgery and could be sidelined until December, a timeline that would rule him out of the opening months of the new Premier League season. Yahoo Sports has separately reported that Arsenal are braced for a lay-off of four to five months.
Saliba was withdrawn before half-time and replaced by Crystal Palace's Maxence Lacroix, having earlier kicked the ball out of play and shaken his head towards fellow centre-back Dayot Upamecano. He is also reported to have told Upamecano that he could no longer bear the pain.
It represents a major setback for Mikel Arteta's side, who are due to defend their Premier League crown without one half of their first-choice central defensive partnership for the foreseeable future. Saliba made 50 appearances in all competitions last season as Arsenal ended a 22-year wait for the title and reached the Champions League final.
Saliba had made clear during the World Cup group stage that he was carrying a long-standing back problem, telling reporters: "I've had some minor niggles for several months. I've been gritting my teeth because there was the Champions League and the Premier League. But the coaching staff are handling it very well.
"The World Cup comes around only once every four years, so you've got to grit your teeth. I'm not at 100 per cent, but there are plenty of players who aren't at 100 per cent either. You can't make excuses."
He had managed the issue through painkillers and a modified training schedule for much of the second half of last season, with the problem reportedly worsening during Arsenal's Champions League final appearance against PSG.
Arsenal are due to face Manchester City in the Community Shield on 16 August, before opening their Premier League campaign against newly promoted Coventry on 21 August. Should he need surgery, Saliba would be a major doubt for both fixtures and a significant chunk of the early season.
France's own World Cup campaign ended with the defeat, Mikel Oyarzabal and Pedro Porro scoring either side of half-time to send Spain through to the final. Didier Deschamps' side, who had been unbeaten in the tournament prior to the semi-final, still have a third-place play-off to come this weekend, though Saliba will take no further part.
Arsenal's medical staff are expected to conduct a full assessment of Saliba once he returns from international duty, with the club's coaching staff having worked closely with the French federation's doctors on managing his condition throughout the tournament.