"An inquiry into the Stonehaven accident has already begun, and we must ensure that any necessary lessons are learned", Sturgeon said, as cited by the SNP political party on Twitter.
Three people have died after a passenger train derailed on Wednesday, following a night of heavy rains. Six other people were taken to the hospital for treatment.
A landslide is believed to have played a role in the incident, which saw the train leave the line before bursting into flames, according to domestic media reports.
Some regions of eastern Scotland were hit with torrential rain overnight that led to flash flooding and landslides. According to the Met Office, more than three inches of rain fell in a matter of hours, as severe thunderstorms brought heavy downpours.