Last month, Ms Ferrier admitted to travelling from Glasgow to Westminster while awaiting a Covid-19 test result, and making the return trip when she knew she had the virus.
The Metropolitan Police said "no further action" will be taken against the Rutherglen and Hamilton West MP because the regulations on self-isolation came into force after she was tested.
Had the MP been found in breach of the rule, it could have resulted in a £10,000 fine being levied against her.
In a statement on their investigation, the Met said detectives investigated the politician's account of her journey.It continued: "Officers considered possible offences including those under Reg 11(2) of the Health Protection Regulations 2020 which relates to self-isolation requirement.
"However, on detailed examination of this new legislation, and following legal advice, it was concluded that this regulation is applicable only after the 28th September 2020.
"In this case the test occurred prior to the 29th September 2020 and therefore the regulation does not apply."
The force said it is taking no further action but has referred the matter to Police Scotland for consideration.
Police Scotland have in turn responded saying it is "aware of the decision" made by the Met, adding: "We will now assess the circumstances and consult with the Crown Office and Procurator Fiscal Service before taking a decision on next steps."
Ms Ferrier faced condemnation for her actions from across the political spectrum.
Scotland's First Minister Nicola Sturgeon described the MP's behaviour as "reckless, dangerous and completely indefensible".House of Commons speaker Lindsay Hoyle urged Ms Ferrier to consider her position, telling ITV News: "An MP is meant to set the standard and, quite rightly, I am angry, the public's angry."
He continued: "Not only did they put the House of Commons at risk, they put public transport at risk [...] It's not acceptable and they should consider their position."
The Prime Minister, on the other hand, refused to comment on whether Ms Ferrier should quit - stating it is a matter for the SNP.
Following Thursday's update on the police investigation, a spokesman for the SNP said: "Police Scotland and the parliamentary standards commissioner are still considering matters.
"It is important that due process is followed and we will not be offering further comment. Ms Ferrier remains suspended from the SNP."