Ms Sturgeon was in attendance at Waverley station in Edinburgh to pay her respects at 9.43am, the time the crash was reported.
Driver Brett McCullough, 45, conductor Donald Dinnie, 58, and 62-year-old passenger Christopher Stuchbury, died after the train derailed after hitting a landslip near Stonehaven following heavy rainfall. A further six people were injured in the incident.
The minute's silence was observed at rail stations across the country, with relatives of the three men gathering in Aberdeen, where an array of floral tributes had been laid.
Ahead of visiting Waverley alongside transport secretary, Michael Matheson, Ms Sturgeon tweeted: “I will join @ScotRail and others in Waverley Railway Station at 09.43 this morning, to remember those who lost their lives in the Stonehaven tragedy one week ago.
"We will remember Brett, Donald and Christopher and hold their loved ones in our thoughts.”
At Glasgow Queen Street, railway staff were among those to pay tribute in the station’s concourse.
Alex Hynes, managing director of Scotrail, said: “Our hearts remain broken and will do for a long time.
"We hope that by coming together as a railway family, along with the local community and people across the country, we can support one another through this horrendous time."
Many English and Welsh stations joined the tribute and the Scottish Parliament also marked the minute's silence.
At London Waterloo, a number of Network Rail staff stood underneath the station's clock in a circle with their heads bowed.
Conservative MP Huw Merriman, chairman of the Commons Transport Select Committee, was among those to pay their respects, alongside a handful of passengers, British Transport Police officers and station staff.
Investigators have said the train derailed and slid approximately 90 metres before hitting and destroying a barrier on the edge of a bridge, leading the front power car and one carriage to fall down an embankment.
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