The train was stopped on Sunday evening at the Brenner Pass in the Alps, the Ministry said in a statement, adding that further procedures are being discussed with the Italian authorities.
"We take the situation in Italy very seriously and are in close coordination with the Italian authorities", Austrian Interior Minister Karl Nehammer said in a Sunday statement.
Nehammer stressed that there is no need to panic in Austria as the country is "well prepared".
Austrian train operator OBB was informed by the Italian State Railways of two people with a fever on the train going to Munich from Venice, according to the Interior Ministry. The train is currently on Italian territory. Train passage through the Brenner Pass has been halted in both directions.
OBB spokesperson Robert Lechner said on Sunday that train service between Austria and Italy was being temporarily suspended because of the coronavirus situation.
"Train journeys via the Brenner are currently not possible. The reason for this is an official ban", OBB said in a statement on its official Twitter account.
Recently, the OBB train operator announced that Austria is resuming railway service to and from Italy.
"The official lock on the Brenner was recently lifted", the Austrian OBB train operator said late on Sunday, adding in another tweet that starting "from tomorrow we can drive over the Brenner again according to schedule. Anyone who does not want to go to Italy can cancel their ÖBB ticket to Italy valid through 24.02.2020 free of charge".
On Sunday, Italy reported the third death from the coronavirus disease (COVID-19). Italy has registered more than 150 coronavirus cases across five of its regions.