The 8.04am CrossCountry service from the capital to Aberdeen came off the tracks at Inverkeilor, between Arbroath and Montrose in Angus.
There were 36 passengers and two crew members on board but no-one was hurt. No reason has yet been officially given for the derailment.
Passengers including a young child clutching a toy were seen climbing down ladders set up by emergency crews to get down from the train after the incident.
It left the locomotive at an angle to the northbound track and blocking the opposite one.
First ScotRail laid on alternative transport for passengers travelling from Aberdeen to Edinburgh and Glasgow after the incident at 9.45am.
The operator said the disruptions are expected to continue until almost midnight and urged travellers to allow extra time for their journeys.
In a statement, the company said: "The front wheels of the train became derailed but the train remained upright."
Rail services were suspended in the area and replacement road transport was arranged immediately after the incident. A full investigation is to be undertaken to determine the cause of the incident.
ScotRail said arrangements for travel today will be similar to those brought in yesterday after the incident.
Services between Aberdeen and Glasgow Queen Street and Edinburgh Waverley were terminating at Montrose and restarting at Dundee, with replacement buses to Dundee from Montrose.
Services from Queen Street and Edinburgh to Aberdeen via Dundee were also terminating at Dundee, with a replacement bus service onward to Aberdeen. A spokesman for Network Rail, which operates track and signalling infrastructure, said "The cause of the partial derailment is being investigated and we are working with the Rail Accident Investigation Branch."
The overnight Caledonian Sleeper service was not disrupted, though passengers travelling from Aberdeen were due to be bussed to Edinburgh to catch the train.
There have been a number of derailments in Scotland in recent years.
In July this year, about 30 passengers and two crew escaped injury after the front carriage of the Newcraighall to Edinburgh service hit a mudslip between Rosyth and Dunfermline amid widespread flooding across Scotland. In July 2011, a ScotRail service derailed near Edinburgh's Waverley Station, although no passengers were on board at the time and it was travelling at low speed.
In one of the most dramatic derailments in recent years, the front carriage of the 6.20 Glasgow-Oban train, which had 64 passengers on board, caught fire and was left dangling over a 15-metre embankment in June 2010. Again, no-one was injured.
In February 2007, the London to Glasgow Virgin Trains service came off the tracks at Grayrigg in Cumbria.
Margaret Masson, 84, from Glasgow, died from multiple injuries in the incident.