The pair were sent off at half-time for the altercation in the 1-0 defeat.
St Johnstone have now concluded an internal investigation into the incident and imposed the "most severe" sanctions "short of summary dismissal".
In a statement the club added that both accept they brought the Perth outfit into disrepute due to the incident.
The statement continued: "The players have accepted the sanctions without question and they wish to apologise unreservedly to the supporters of the club for their behaviour.
"Both players have expressed a desire for a proportion of the fines to be utilised for free bus travel for supporters to the remaining away matches this season and the club is in full agreement with this request.
"The players will now return to training and playing duties where they can channel their energies into contributing to the continued success of the club."
St Johnstone have fined Danny Swanson and Richard Foster four weeks' wages for their on-field bust-up against Hamilton Academical.