The 27-year-old has since apologised for what he described as a “severe lack of judgement”.
Possession of nitrous oxide – also known as laughing gas – for recreational use has been a criminal offence in the United Kingdom since 2023 and can result in a two-year prison sentence for repeat offenders.
“We’ve suspended him for Monday’s game,” said Postecoglou at his pre-match press conference on Thursday.
“The door is open for him and hopefully we can help him to realise the decisions he makes impact more than just him.
“Hopefully it allows him to make better decisions moving forward.”
Bissouma, who joined Spurs from Brighton for £30m in 2022, had played 45 minutes in Spurs’ friendly loss to Bayern Munich on Saturday afternoon.
Later that day he posted a video of himself on social media which showed him inhaling from a balloon.
“I want to apologise for these videos. This was a severe lack of judgement,” said Bissouma in a statement.
“I understand how serious this is and the health risks involved, and I also take my responsibility as a footballer and role model very seriously.”
In more positive news for Postecoglou, Dominic Solanke is in line to make his debut as the Premier League gets underway this weekend.
Solanke has joined from Bournemouth in a deal that could rise to £65 million ($83 million) after scoring 19 Premier League goals last season.
“Thankfully it’s what we expected. He’s a top pro and a good guy, he’s settled into the dressing room really well,” added Postecoglou.
“Football-wise you can see he has all the attributes we need. He still needs time to fit in. He’s fitting in well with the group and training. We’ve still got a couple of training sessions to go but he’s doing well. He should be (available on Monday).”
Tottenham finished fifth in Postecoglou’s first season as they faded after a stunning start to the Australian’s reign.
The former Celtic boss believes his side are better placed to qualify for the Champions League this season.
“We feel a lot more settled and better prepared for what’s ahead,” he said.
“There were a lot of unknowns last year at this time. Having said all that, it didn’t stop us from having a great start to the season.
“The pleasing thing is pretty much everyone on the list is available and that will be important for us. After the (September) international break, Europe starts and the Carabao (League) Cup, so we’ll need all our players.”
© Agence France-Presse
Photo: Alvaro Medranda/Icon Sport via Getty Images