ScotRail, who deny the allegations, has posted on Twitter in recent days informing customers of impending disruption on Sunday as a result of strike action by the RMT union over rest day payments.
Mark Ruskell, the transport spokesman for the Scottish Greens urged the operator to resolve the dispute.
"The Transport Secretary must make it immediately clear to (ScotRail operator) Abellio that it has a duty to its staff, and passengers, to resolve this situation," he said.
"It is a problem of the operator's own making and one that it has an obligation to fix.
"Ministers are ultimately responsible for the operation of our railways and cannot sit back while the private operator attacks the frontline staff who have gone above and beyond during the pandemic to keep our railways running.
"The Scottish Greens are strongly supportive of moves to bring ScotRail entirely into public hands, but until that happens, Government must keep pressure on the private operator to respect their industrial obligations and treat their workers with respect."
The disruption is expected to hit Scotland fans, who will be returning north of the border over the weekend following the men's national team game in London on Friday night.
David Simpson, the operations director at ScotRail, accused the RMT union of spreading "misinformation" after they accused Scotrail of trying to turn the public against the striking workers.
He said: "Hundreds of fans are expected to travel back to Scotland on Sunday, after the match on Friday, and we have a duty to let people know that when they do return, there will be very few services operating due to strike action by the RMT.
"You would think the Scottish Greens would realise that we are meeting our obligation to customers by advising them to make sure they have arranged their onward travel from Glasgow Central and Edinburgh Waverley and they would not repeat the continuing misinformation put out by the RMT.
"The RMT strike is completely wrong, divisive and is putting the jobs of clear thinking, reasonable colleagues at risk."