The rockfall at Winchburgh in West Lothian followed high water levels under a bridge between Linlithgow and Winchburgh halting trains earlier.
The ScotRail Alliance with Network Rail stressed the remaining wall was safe.
However, it could not say whether it could have been weakened by the installation of a pylon adjacent to the landslip, which supports overhead wires as part of electrification of the line, which was completed in October.
Buses running every half hour are replacing trains between Linlithgow and Edinburgh Park.
Trains between Linlithgow and Glasgow Queen Street have been reduced to half hourly.
Dunblane-Edinburgh trains have been replaced by an hourly shuttle bus from Edinburgh Park, with no trains running east of Falkirk Grahamston.
Disruption is expected to continue until at least the rest of the day.
ScotRail said it would be "until further notice".
ScotRail tweeted: "Engineers are on site assessing the damage and putting plans in place to reopen the railway.
"Embankment needs to be inspected also to ensure it's safe to run trains.
"More than just shifting a few rocks involved."
ScotRail urged Edinburgh-Glasgow passengers to use one of the three other lines between the cities instead, including via Shotts and Carstairs.
Earlier, rising levels under a bridge on the nearby Niddry Burn halted trains when they breached a red marker.
There was also disruption on a fourth Edinburgh-Glasgow route via Airdrie because of flooding between Bathgate and Livingston North.
A pump failed after water engulfed tracks at Starlaw, with disruption expected until 3pm.
Transport minister Humza Yousaf tweeted about the landslide: "It should be noted that safety is the main issue here.
"Simply a matter that cannot and will not be compromised on.
"As the picture demonstrates, landslips present a very real danger to our rail services.
"Plan will be to inform people before the evening peak of service disruptions."
However, passengers expressed anger at the lack of information from ScotRail.
Máire Dobbin tweeted: "A bit of communication from @ScotRail in Linlithgow this morning would’ve been helpful, it was absolute chaos!"
Sports event manager Susan Murrin tweeted: "I was on the 0730 from Ed-Queen St this morn. No news for ages as we sat between Ed Park & Linlithgow.
"Train sent back to Ed and then no info to say that services were now being diverted.
"On the same train for 2h45 mins - minimal info and no contact with on train staff."
A ScotRail Alliance spokesman said: “We apologise to customers for any disruption this will cause to their day, and share their frustration, however their safety is our number one priority.
“Our engineers are on the ground assessing the damage and doing everything possible to keep people moving."
Elsewhere, a landslip at Kirkconnel in Dumfries and Galloway overnight shut the line between Kilmarnock and Dumfries.
Meantime, the Fort William-Mallaig line is expected to stay closed until next Monday after a 1,000-tonne landslip between Lochailort and Glenfinnan on Monday.
Extensive survey work to check the stability of the slope above the line at Loch Eilt has been completed.
Engineers have now started to dig out the derailed train and clear the tracks.
Extra drainage will be installed and stabilisation work done on the slope above the line.