ScotRail said the minimum fare was not a penalty or a fine but rather the fare charged when someone travels without buying a ticket beforehand where they could have reasonably done so.
It said no personal details would be taken and existing processes for deliberate fare evasion or non-payment remain unchanged.
The train operating company estimates fare evasion costs the state-owned railway more than £11m each year.
The change is also expected to reduce anti-social behaviour on trains, which ScotRail said is often linked to a small minority of passengers travelling without a ticket.
“A period of education” for passengers was launched on 1 April before the full scheme was rolled out.
Phil Campbell, ScotRail’s customer operations director, said: “We know most people are honest and pay the correct fare but the minority who don’t are costing the railway millions of pounds each year.
“The success of our new policy will not be measured by the number of minimum fares we hand out, but by the amount of people who buy a ticket before getting on board a train.”
He praised the success of the education campaign and added: “We look forward to more and more people doing the right thing and buying before they board.”
