A statement by the Perth club also came with a warning from Police Scotland that fans breaking the law at McDiarmid Park risk spending the Christmas period "locked up".
St Johnstone said it had taken the decision because of its belief that flags and banners have been used to conceal flares and other pyrotechnics in football grounds, adding that Celtic have agreed to the move.
The decision was announced after it emerged Celtic have lifted bans on most of the notorious Green Brigade section of fans who had been suspended as part of the investigation into damage at Motherwell's Fir Park stadium earlier this month.
The club has written to the most of the 128 suspended supporters telling them they are free to attend games while the probe is ongoing. It is understood those not offered a return have been identified as being associated with the Motherwell damage.
A Celtic spokesman said: "A number of suspensions remain in place. All investigations are very much ongoing and whilst this is the case it is reasonable to lift the suspension for some season ticket holders." However, most have snubbed the invitation due to their section having been broken up by the club.
The flags ban emerged after social media exchanges between Celtic's fans' liaison officer and supporters and was confirmed in a statement by St Johnstone.
The Perth club said: "Supporters will be aware that, regrettably, there has been a significant increase in the letting off of flares, smoke bombs and other pyrotechnics at games across the country this season.
"These are inherently unsafe not only for those around the devices but also for spectators in general, particularly those who suffer from breathing disorders. They also have the potential to set seats alight and burn flags.
"St Johnstone FC and Celtic FC fully support Police Scotland in their attempts to eradicate this nuisance from our game and as part of the planning process for this match between the three parties and other agencies, and as there have been several instances of flags being used as cover for the igniting of these devices, a decision has been taken that, for this specific fixture, flags and banners will not be permitted inside McDiarmid Park. Fans are asked to be considerate of this requirement in the interest of their own safety and the safety of others."
A police statement said: "Police Scotland has been working closely with both clubs and other agencies to ensure everyone enjoys the game in true festive spirit. But we also serve notice that anyone who falls foul of the law runs the risk of spending part of the Christmas period locked up."