The move will come five weeks after the main Edinburgh-Glasgow route was closed near Polmont, west of Linlithgow, because of a canal burst.
The Dundee-Stonehaven line was blocked the same day – 12 August – by a derailment in which three people died.
The Polmont line is expected to remain closed for several more weeks, while the Stonehaven route is not likely to re-open until at least next month.
ScotRail said the Edinburgh-Linlithgow service would call at Edinburgh Park and Haymarket.
Replacement buses between Falkirk Grahamston and Linlithgow will continue.
Glasgow-Edinburgh passengers can use other lines via Bathgate and Shotts.
A 300m section of line was badly damaged when the Union Canal bank collapsed, engulfing the line and gouging a large hole under the tracks on 12 August.
Overhead power masts were also washed away and dozens of uprooted trees were strewn across the tracks.
ScotRail operations director David Simpson said: “The unprecedented rainfall near Polmont had a severe impact from which we’re still trying to recover.
“Network Rail’s specialist engineers are working as quickly as possible to complete repairs to the track and railway infrastructure near Polmont that was caused by flood damage.”
The Edinburgh-Montrose shuttle, which will run to and from Dundee on Sundays, follows the introduction of an Aberdeen-Stonehaven shuttle last week.
The line is blocked by a landslip caused by rock and gravel being washed onto the track by heavy rain which derailed an Aberdeen-Glasgow train.
Replacement buses between Dundee and Aberdeen will continue.
A 600-tonne crane started lifting the wrecked carriages from the line yesterday.
Engineers will then assess the extent of damage to the tracks and a bridge hit by the train as it crashed.
Driver Brett McCullough, 45, conductor Donald Dinnie, 58, and passenger Christopher Stuchbury, 62, died in the incident, in which when the 6:38am Aberdeen to Glasgow Queen Street train derailed.
Two separate investigations are continuing into the incident,