However, commuters will see peak fares and season tickets going up by 1 per cent from 2 January.
This compares to a 2.5 per cent rise this year.
The increase will add some 25p to the £23.10 peak (“anytime”) return between Edinburgh and Glasgow.
Peak fares on cross-Border trains run by Virgin Trains on the east and west coasts, CrossCountry and First TransPennine Express will rise by 1 per cent. The firms are also expected to raise off-peak fares.
Ticket price increases for the following year are based on the July rate of the Retail Prices Index (RPI) measure of inflation, which was revealed today as 1 per cent.
But ScotRail’s buy-on-the-day off-peak singles and returns change by RPI -1 per cent, so will remain unchanged.
These account for four in ten journeys.
ScotRail said it would announce any changes to its advanced purchase off-peak fares, such as super off-peak and advance tickets, in the autumn.
Infrastructure secretary Keith Brown said: “The Scottish Government wants to see more people take the train, and recognises that prices have to be affordable and fair.
“The continued freeze on the cost of off-peak rail fares, for the third consecutive year, will help encourage passengers to shift to more lightly-used services where possible.”