Neither full-back was spotted in the Lilywhites' open training session on Thursday, where Postecoglou's troops practised in front of supporters at the Tottenham Hotspur Stadium, raising fears about their availability for the weekend.
It was reported that both men were carrying issues which would require assessment in the coming hours, although Udogie was unable to complete the full 90 minutes of last weekend's 2-1 win over Brighton & Hove Albion.
During his post-game press conference, Postecoglou admitted that he was not sure if Udogie's problem was cramp or something more serious, but the Spurs boss has now revealed that the Italian tweaked his knee.
In addition, Porro has been ruled out with a strain sustained in a training session, and the right-back could potentially miss a couple of weeks of action, which may also rule him out of the London derby with Crystal Palace on March 2; the Lilywhites have no fixture scheduled for next weekend due to Chelsea's participation in the EFL Cup final.
Speaking to Tottenham's media channels, Postecoglou said: "We've had a couple of setbacks this week. Destiny jarred his knee a little bit in last week's game, don't think it's anything too serious but he'll miss tomorrow.
"Hopefully with no game next week that's all he misses. Pedro picked up a strain in training, we'll get some further information but fair to say he'll miss tomorrow, maybe a couple of weeks for him."
In addition to Porro and Udogie - whose spots should be filled by Emerson Royal and Ben Davies on Saturday - Postecoglou also revealed that backup goalkeeper Fraser Forster had joined the Lilywhites' injury list.
The experienced shot-stopper was also absent from the open training session on Thursday, and it has now been announced that he is nursing a foot fracture, which could sideline him for a couple of months.
"The big one is Fraser Forster. He picked up a knock in training - a fracture in his foot so he's longer-term, couple of months for him. Disappointing for those three lads."
With Forster unable to fulfil his backup duties, either Brandon Austin or Alfie Whiteman - who has seemingly made a full recovery from a serious ankle problem - will act as Guglielmo Vicario's deputy this weekend.
Forster, Udogie and Porro make up three of Spurs' five definite absentees for the visit of Wolves, as Manor Solomon (knee) and Ryan Sessegnon (thigh) are still undergoing their recovery programmes.
Giovani Lo Celso was also missing from the squad to face Brighton due to his thigh injury, but he joined his teammates for open training this week and could make his comeback against Gary O'Neil's side.
The Lilywhites enter gameweek 25 sat one point clear of Aston Villa in fourth place in the Premier League table, but they have been beaten in their last two meetings with Wolves, including an agonising late 2-1 loss at Molineux in November.