Images appeared to show Drissa Traore, Brandon Ormonde-Ottewill and Jeremy Balmy taking the legal high, commonly known as laughing gas, via balloons.
"The club have already started an internal investigation into the trio's recent conduct," a club statement said.
"They will not be considered for selection during this process."
The Robins, who are 15th in the table, lost 2-0 at Oldham Athletic on Tuesday.
Swindon have not won in six games since head coach Luke Williams signed a five-year deal on 9 March, following a run of six wins from 10 in interim charge.
Between 2006 and 2012, 17 people in the UK died after taking nitrous oxide.
A new law designed to crack down on legal highs was due to come into force but has been delayed.
Then-Liverpool boss Brendan Rodgers said he would speak to England forward Raheem Sterling, now at Manchester City, after he was pictured allegedly taking nitrous oxide in 2015.
Swindon Town have suspended three of their players and are investigating reports they inhaled nitrous oxide on a live social media video on Wednesday.