The U-turn for the Jacobite comes just a week after West Coast Railways said the daily Fort William-Mallaig service would begin on 6 April.
A spokesman said: “We made the decision with great regret.
“Many of our passengers come from all corners of the world to travel on the train.
“However, the effect of this devastating virus changes by the day.
“We will make a further announcement on 17 April about what will happen in May.”
Passengers on trips next month are being offered a full refund or they can re-book for a later date.
The company has also cancelled four trips on its Northern Belle train including one to Edinburgh from Manchester, Huddersfield and York on 17 April.
Refunds are being offered.