The figure amounts to 3.25 per cent of its workforce of 5,300, The Scotsman has learned.
That is far higher than other operators which have provided figures.
ScotRail staff to have been recently affected are believed to have included train conductors and cleaners, catering and station staff in Aberdeen, according to an industry source.
The Scotsman understands the operator will reduce services from 80 to around 65 per cent of normal from February 1.
However, this is largely to reflect passenger numbers being 90 per cent down on normal rather than any staff shortages.
A ScotRail spokesperson said: “We have around 3.25 per cent of our staff currently absent due to Covid-19.
"That includes those who are currently shielding, have tested positive or are isolating due to close contact.
“There is currently no specific issue at Aberdeen and most staff have now resumed duties.
“There are no other specific outbreaks of note currently.”
The firm has suspended driver training because train cabs are too small for the required social distancing.
Bus operator First said there had been a Covid outbreak at its Midland Bluebird depot in Bannockburn affecting an unspecified number of its staff and forcing services to be reduced.
It has not also disclosed the number of workers affected by the virus at its other main Scottish operations in Glasgow and Aberdeen.
West Coast Motors said “only a handful of drivers – about 1 per cent” were shielding and “the odd isolated case of those who have had to self isolate”.
Fellow bus operator Stagecoach said only that the number of affected staff was “small”.
West coast ferry operator CalMac said it had about 47 staff off work among its 1,800-strong workforce.
The company said that comprised 1.7 per cent of staff shielding and 0.9 per cent self isolating.
NorthLink, which operates ferries to Orkney and Shetland, said four of its 500 staff had currently tested positive for Covid – or 0.8 per cent.
Among other train operators, Caledonian Sleeper said it had one positive case among its 200 staff (0.5 per cent)
LNER said it had “very low” numbers of staff affected but Avanti West Coast said it was “unable to give figures”.
Glasgow-based airline Loganair said four of its 780 staff were self-isolating (0.5 per cent).
Highlands and Islands Airports is believed to be experiencing “minimal” Covid cases and numbers of staff isolating, while Edinburgh and Glasgow airports did not respond to enquiries.
The Scottish Government’s Transport Scotland agency said one of its 600 staff and consultants was currently off after testing positive for Covid (0.2 per cent).
A ScotRail spokesperson said of its suspended training: “There will be an obvious impact on getting our drivers through training.
"There is a backlog as we have not been able to train drivers to the normal timescales.
“It’s impossible to say with any certainty what lies ahead of us, as the restrictions change and the vaccination programme is rolled out.
“As has been the case since March 2020, we are delivering a reliable and robust timetable, and we aim to continue doing that.”