The 32-year-old defender, earning his 100th cap in what should have been a landmark appearance, went down injured late in the second half and had to be replaced after 72 minutes.
Wales manager Rob Page confirmed that medical staff would assess the extent of the problem in the coming days.
Davies' setback is another blow for Spurs boss Thomas Frank, who is already without several key players. "It's never good to see one of your experienced players go off like that," Frank said before adding that the club will "wait for further updates" from the Welsh medical team before determining the severity of the injury.
The London club are already dealing with a growing injury list. Midfielder Yves Bissouma was stretchered off while playing for Mali against Madagascar, adding to Frank's concerns.
James Maddison, Dejan Kulusevski and Dominic Solanke also remain sidelined as they continue their recoveries from respective injuries.
There is, however, some encouragement for Spurs. Striker Randal Kolo Muani is expected to return to full training after the international break, having missed recent matches with a dead leg.
Tottenham, who are currently pushing for a top-four finish in the Premier League, return to domestic action on Sunday, 19 October, when they host Aston Villa at Tottenham Hotspur Stadium.
Frank will be hoping his side can regroup and recover in time for what promises to be another crucial test in their season.