Jay Rodriguez left Saturday's match on a stretcher with apparent damage to the ligament in his knee.
Southampton lost the match to Man City 4-1.
"We do not know the extent of the problem yet because we have not completed an assessment, but it is not looking good," Mauricio Pochettino said. "All the players are really upset, they can see how severe the injury is."
Rodriguez has only been capped once by England but had been making a strong claim for a spot on England's World Cup team.