Margaret Ferrier learned that her test was positive on Monday after she had spoken in Britain's parliament at Westminster.
"On Monday evening I received a positive test result for Covid-19. I travelled home by train on Tuesday morning without seeking advice. This was wrong and I am sorry," she said in a statement.
Scottish National Party (SNP) leader Ms Sturgeon lambasted Ferrier for her "utterly indefensible" actions.
"It's hard to express just how angry I feel on behalf of people across the country making hard sacrifices every day to help beat Covid," Ms Sturgeon said on Twitter.
"The rules apply to everyone and they're in place to keep people safe."
This is utterly indefensible. It’s hard to express just how angry I feel on behalf of people across the country making hard sacrifices every day to help beat COVID. The rules apply to everyone and they’re in place to keep people safe. @Ianblackford_MP is right to suspend the whip https://t.co/9rgWpPKrOeAdvertisement
— Nicola Sturgeon (@NicolaSturgeon) October 1, 2020
The SNP's Westminster leader Ian Blackford said earlier that he was suspending Ms Ferrier.
Scottish police said Ms Ferrier had contacted them earlier today about the journey she made after testing positive for coronavirus.
"We are looking into the circumstances and are liaising with our colleagues in the Metropolitan Police Service," Police Scotland said, referring to London's police force.
It is mandatory in England for people to self-isolate if they test positive for Covid-19, with fines of £1,000 (€1,097) for those who breach the rules.
In May, UK Prime Minister Boris Johnson's most senior adviser Dominic Cummings refused to quit after it emerged he had driven 250 miles (402 km) from London to northern England when all but essential travel was forbidden. -Reuters