It follows an overwhelming majority of conductors and other staff voting for the action over being paid less than drivers for working on days off.
The union has instructed its 3,500 members involved not to volunteer for overtime or work on "rest days" from midnight on 10 October "until further notice".
It has said this would cause "massive" disruption because ScotRail is short of staff.
RMT Scotland organiser Mick Hogg said: "Our railway will come to a grinding halt if overtime is banned - no question about this."
BACKGROUND: RMT warns ScotRail will 'grind to halt' after vote to ban overtimeGeneral secretary Mick Cash said: "It cannot be right that the company seem to value one group of workers over another.
"Their approach to the rest day working payments, where they have offered driver grades enhanced arrangements is nothing short of discriminatory.
"A driver working rest days is no different than any other member of front line staff working rest days.
"All staff should be treated equally and fairly."
The union is holding a separate ballot among train maintenance staff.
Train conductors and other RMT members such as station staff are paid between £112 and £140 for working their rest days compared to £300 for drivers.
ScotRail has said 140 new "front-line roles" will "significantly reduce the need for rest day working".