They remain mandatory in trains, at stations and in indoor public spaces such as shops, unlike in England.
However, ScotRail said it was British Transport Police’s (BTP) responsibility to ensure compliance.
Operations director David Simpson told BBC Radio Scotland's Good Morning Scotland programme: "We're not expecting our staff to enforce it.
"Our staff can often be in very difficult position in that respect, particularly on evening services where customers are perhaps more refreshed than usual.
"What we don't want to do is put staff into difficult, challenging, potentially upsetting environments."
ScotRail said announcements in trains and stations would remind passengers of the requirement to wear face coverings.
Mr Simpson said CCTV monitoring had shown "very high" compliance.
He said the train operator would work with BTP where there were "trouble spots".
However, physical distancing on trains was scrapped on Monday, so passengers are now free to use every seat or stand.
A BTP spokesperson said: “As has been the case throughout the pandemic, our officers will continue with the ‘4Es’ approach of engage, explain, encourage and, as a last resort, enforce any coronavirus legal requirements.
"As our jurisdiction covers three countries [Scotland, England and Wales], our officers police different laws every day, including throughout the pandemic, and are used to dealing with any challenges this presents.”
ScotRail said it had also removed its prohibition on passengers consuming food and drink on trains on Monday, which it said was introduced with compulsory face coverings in June last year.
A spokesperson said the move coincided with the resumption of catering on some services on the Glasgow-Oban/Mallaig West Highland Line.
All ScotRail catering had been suspended since last year.
Among bus operators, the jointly-run Borders Buses, Citybus in Glasgow and West Coast Motors in Argyll and Bute said they had seen a slight drop in face covering-wearing compliance this week, but “nothing significant”.
They had not needed to involve police over non-compliance.
The firm said it had been praised by passengers for insisting on their use on the English legs of cross-Border journeys.
First Bus, the main operator in Glasgow and Aberdeen, said compliance levels were “generally still very high” and passengers were in the main glad of extra capacity the scrapping of physical distancing had brought.
A spokesperson said: “They seem to have an understanding and are willing to wear a mask as part of routine now.
“We are following Scottish Government guidance for our staff to engage, explain and encourage customers to wear face coverings.
"If someone isn’t wearing a face covering, the driver will remind them of this requirement.”