Bissouma posted a social media video on Saturday in which he was seen inhaling from a balloon containing the Class C drug known as laughing gas.
Mali international Bissouma is set to face an internal club investigation and could face punishment for his actions.
Nitrous oxide possession for recreational use has been a criminal offence in Britain since 2023 and can result in a prison sentence as part of the Government's anti-social behaviour action plan.
"I want to apologise for these videos. This was a severe lack of judgement," Bissouma said in a statement on Monday.
"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."
A Tottenham spokesman added: "We are looking into the events. This will be dealt with as an internal matter."
It is possible to use the gas for legitimate reasons, such as in catering for pain relief during labour.
Bissouma joined Tottenham from Brighton in 2022 and has made 56 appearances for the club, including 26 starts during the 2023/24 campaign.
He played for 45 minutes of Tottenham's friendly against Bayern Munich on Saturday in their final warm-up before the start of the Premier League season at Leicester on August 19.
