Margaret Ferrier was suspended by the Scottish National Party after her journey came to light, but has so far ignored calls to resign as an MP.
The MP travelled between Glasgow and London twice while suffering from symptoms of coronavirus, the second time after she was told she had Covid-19.
A Police Scotland spokesperson said: “We can confirm that officers today arrested and charged a 60-year-old woman in connection with alleged culpable and reckless conduct.
“This follows a thorough investigation by Police Scotland into an alleged breach of coronavirus regulations between 26 and 29 September 2020.
“A report will be sent to the procurator fiscal and we are unable to comment further.”
SNP leader Nicola Sturgeon was among those who called for her to stand down after she confessed she had made the same five-hour train journey twice while carrying the virus.
As well as travelling to and from the House of Commons, social media posts also showed she had visited businesses in her constituency while suffering symptoms.
They included a gift shop, a gym and a salon, which she said she had “popped into” to wish the team well.
Ms Ferrier has referred herself to the Commons standards commissioner, who can trigger a process known as a “recall” vote if she suspends Ms Ferrier from the house for a total of more than 10 days.
Under the rules of recall, a by-election can be called if more than one in ten voters in Ms Ferrier’s constituency sign a petition.
Ms Ferrier currently sits as the independent MP for Rutherglen and Hamilton West.