Van de Ven was forced off in the 14th minute of Wednesday’s 2-1 win over Manchester City in the Carabao Cup.
The Dutch defender was emotional as he left the pitch but is due to return after the international break this month.
“He’s pulled his hamstring. It’s not very serious, but probably after the international break for him,” revealed Spurs boss Postecoglou.
“He was obviously disappointed and he was looking forward to the (Manchester City) game so emotional but it’s definitely not as bad as the last time which took him out for a while.”
When Van de Ven left in midweek, it was reminiscent of when he injured his hamstring last year against Chelsea, which ruled him out for two months, but he will now focus on the league clash against Manchester City on November 23.
Christian Romero and Timo Werner were also brought off during the cup win and will be assessed ahead of Sunday’s Premier League game at home to Villa.
Spurs captain Son Heung-min missed the game after a setback with a recent thigh injury but returned to training on Friday.
Postecoglou added: “The others were Romero and Werner, but at the moment there is still a chance for the weekend.
“The son is training today. If he trains tomorrow, he should be fine.”