The 20-year-old midfielder, who had started strongly at the Liberty Stadium, suffered the injury in a 2-1 victory over Millwall before the international break.
After scoring once and coming up with an assist from four games, he will have to wait until the new year to add to those tallies.
Swansea boss Steve Cooper said on Gibbs-White: "He's out for three months. Unfortunately, he's got a stress fracture in his foot. It's a blow for everybody. He was doing so well for us.
"We brought him here because we thought he was going to be an important part of the team, but these things happen and we have to work hard with him to try and get him fit.
"In the meantime, we've still got enough players to go and be more than competitive in any game that we play."
Gibbs-White added: "Absolutely gutted to be out after a good start to the season but I will be back stronger and ready to compete."