A leaked memo from the party leader’s office said it does not want to see the industrial action go ahead, and accused the Government of failing to engage in any negotiations.
But it said shadow cabinet members “should not be on picket lines”, and asked them to speak to team members to remind them of this.
Thousands of members of the Rail, Maritime and Transport (RMT) union at Network Rail and 13 train operators will walk out on Tuesday, Thursday and Saturday, in the biggest outbreak of industrial action on the railways for a generation.
Services across the UK will start to be affected from Monday evening, with just one in five trains running on strike days, mainly on main lines and only for about 11 hours.
Talks between the RMT and Network Rail were still being held on Monday evening, just hours before the start of the first strike, but the row remains deadlocked, with all sides blaming each other for the lack of progress.
The RMT and Unite are also holding a 24-hour walkout on London Underground which will cause huge disruption to the Tube.
Sharon Graham, general secretary of Unite, lashed out at Labour over the reports regarding the leaked memo.
She told the PA news agency: “The Labour Party was founded by the trade unions and we expect Labour MPs to defend workers, by words and by actions. To instruct Labour MPs not to be on picket lines with workers speaks volumes.
“You don’t lead by hiding. No-one respects that. It’s time to decide whose side you are on. Workers or bad bosses?”
Manuel Cortes, general secretary of the Transport Salaried Staffs’ Association, said: “This is ridiculous nonsense from the party which was created by trade unions. Solidarity is what our movement is all about.”
The memo, seen by Politics Home, said frontbenchers should “expect severe disruption this week as the result of industrial action by the RMT”.
“We have robust lines. We do not want to see these strikes to go ahead with the resulting disruption to the public. The government have failed to engage in any negotiations,” it said.
“However, we also must show leadership and to that end, please be reminded that frontbenchers including (parliamentary private secretaries) should not be on picket lines.
“Please speak to all the members of your team to remind them of this and confirm with me that you have done so.”
Labour declined to comment.