Scotrail said damage to overhead electric wires led to a series of delays and cancellations on the services to Edinburgh.
Passengers hoping to watch Scotland take on Wales in the Six Nations reported overcrowded trains and queues at Queen Street station in Glasgow.
The rail firm said disruption was expected until around 15:00.
It affected services between Helensburgh and Edinburgh, and between Milngavie and the capital, via Airdrie.
They urged travellers to use their website to check on individual journeys and they said tickets could be used on some bus and tram services.
A spokesman for the ScotRail Alliance said trains were running again but the earlier disruption had a knock-on effect on services.
He said: "Due to a fault with the overhead wires in the Haymarket area services were disrupted this morning. We tried to keep customers moving by sourcing replacement buses and arranging for valid train tickets to be used on First and Lothian Buses.
"Our engineers worked as fast as possible to fix the fault and return services to normal.
"We apologise for any inconvenience caused by this disruption and remind customers delayed more than 30 minutes, they are entitled to compensation under our Delay Repay guarantee provided they keep hold of their tickets."
They issued the following advice to passengers.
Rugby fans relying on trains to get to Murrayfield faced severe disruption to their journeys.