The Lilywhites return to top-flight duty on the back of an unexpected 2-1 triumph over Manchester City in the last 16 of the EFL Cup, but the beating of Pep Guardiola's side came at a cost.
Key centre-back Van de Ven was in tears as he was substituted with a hamstring injury in the first half, having already missed around two months of the 2023-24 campaign with a similar concern.
Van de Ven's reaction suggested that he would be set for a spell on the sidelines, and speaking to the media on Friday, Postecoglou confirmed that he would likely spend at least a couple of weeks out.
"Micky has sort of strained a hamstring. It's not too serious but we're probably looking at after the international break," the Australian said at his pre-game press conference.
Which Tottenham games will Van de Ven miss?
In addition to Sunday's visit of Villa, Van de Ven will be unavailable for Tottenham's next Europa League game away to Galatasaray next Thursday, as well as their Premier League home clash with Ipswich Town on November 10.
Van de Ven is also unlikely to be selected for the Netherlands squad for their upcoming contests against Hungary and Bosnia-Herzegovina in the UEFA Nations League, but he could very well make his comeback against Man City on November 23.
The Dutchman was not the only casualty of that win for Tottenham, as Postecoglou was also forced to bring off Cristian Romero and Timo Werner, who opened the scoring on Wednesday with his first of the season.
Postecoglou played down the severity of their issues at full time, though, explaining that Romero's change was for precautionary reasons and Werner was likely suffering from fatigue rather than anything more sinister.
The Spurs boss is keeping his fingers crossed that the pair will be OK for Sunday, adding: "On Timo and Cristian, at the moment, there's still a chance for them for the weekend."
Will Son be available for Villa game?
While there is a slim chance that Werner will not make the cut, Son Heung-min could be a like-for-like swap for the German on the left flank, as the South Korean has a good chance of being back in action on Sunday.
The 32-year-old has sat out Spurs' last three games with a thigh issue, which he picked up in the 4-1 win over West Ham United soon after recovering from a previous hamstring concern.
Postecoglou had a positive update to share on Son's condition, though, saying: "Sonny has trained today. If he trains tomorrow, he should be okay for the weekend."
There was no word on whether Djed Spence (groin) will be available for Sunday's game, though, while Wilson Odobert will definitely miss out following a thigh setback.
Spurs sit eighth in the Premier League table before the visit of fourth-placed Villa, whom Son boasts an impressive individual tally against ahead of his prospective return to action.