Ms Ferrier said she took a test on Saturday afternoon after experiencing “mild symptoms”, meaning she should have self-isolated, before travelling by train to London on Monday.
The MP then spoke in the coronavirus debate in the House of Commons on Monday and, by her account, tested positive for Covid-19 that evening.
"This related to her actions earlier this week, including a train journey on Tuesday, 29 September, between London and Glasgow, following a positive Covid-19 test.
"Following consultation with Police Scotland, officers from the Metropolitan Police, working with British Transport Police, are conducting an investigation into potential offences."
The Met added that the Parliamentary Commissioner for Standards has also been informed